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Ch 10

If we are testing for the difference between the means of two paired populations with samples of n1 = 20 and n2 = 20, the number of degrees of freedom is equal to:

]

CH 13

• A test is conducted to compare three different income tax software packages to determine whether there is any difference in the average time it takes to prepare income tax returns using the three different software packages. Ten different persons’ income tax returns are done by each of the three software packages and the time is recorded for each. The computer results are shown below.

Based on these results and using a 0.05 level of significance which is correct regarding the primary hypothesis?

Answer: The three software packages are not all the same because p–value =2.66E–5 is less than 0.05.

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• A study was recently conducted to see whether the mean starting salaries for graduates of engineering, business, healthcare, and computer information systems majors differ. A random sample of 8 graduates was selected from each major. The following chart shows some of the results of the ANOVA computations; however, some of the output is missing. Given what is available, the proper conclusion to reach based on the sample data is that the population means could be equal using a 0.05 level of significance.

• A national car rental agency is interested in determining whether the mean days that customers rent cars is the same between three of its major cities. The following data reflect the number of days people rented a car for a sample of people in each of three cities. Given this information, the correct null and alternative hypotheses are:

CH14

• A random sample of two variables, x and y, produced the following observations:x y
19 7
13 9
17 8
9 11
12 9
25 6
20 7
17 8
• Test to determine whether the population correlation coefficient is negative. Use a significance level of 0.05 for the hypothesis test.

Answer: Because t =-9.895 < -1.9432, reject the null hypothesis. Because the null hypothesis is rejected, the sample data does support the hypothesis that there is a negative linear relationship between x and y.

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If a sample of n = 30 people is selected and the sample correlation between two variables is r = 0.468, what is the test statistic value for testing whether the true population correlation coefficient is equal to zero?

The following regression output is available. Notice that some of the values are missing.

Given this information, what percent of the variation in the y variable is explained by the independent variable?Approximately 57 percent

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A correlation of -0.9 indicates a weak linear relationship between the variables.

False

A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected and the following regression results were observed:

SUMMARY OUTPUTGiven this output, the point estimate for the average tip per dollar amount of the bill is approximately \$0.21.True

You are given the following sample data for two variables:

Y X
10 100
8 110
12 90
15 200
16 150
10 100
10 80
8 90
12 150

Based upon these sample data, and testing at the 0.05 level of significance, the critical value for testing whether the population correlation coefficient is equal to zero is t = 2.2622.

A study was recently done in which the following regression output was generated using Excel.

SUMMARY OUTPUTGiven this, we know that approximately 57 percent of the variation in the y variable is explained by the x variable.True

When constructing a scatter plot, the dependent variable is placed on the vertical axis and the independent variable is placed on the horizontal axis.

True

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If it is known that a simple linear regression model explains 56 percent of the variation in the dependent variable and that the slope on the regression equation is negative, then we also know that the correlation between x and y is approximately -0.75.

True

The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. The first observations in the sample for y and x were 300 and 18, respectively. Given this, the residual value for the first observation is approximately 81.6.

False

Two variables have a correlation coefficient that is very close to zero. This means that there is no relationship between the two variables.

False

A random sample of two variables, x and y, produced the following observations:

x y
19 7
13 9
17 8
9 11
12 9
25 6
20 7
17 8

Test to determine whether the population correlation coefficient is negative. Use a significance level of 0.05 for the hypothesis test.Because t =-9.895 < -1.9432, reject the null hypothesis. Because the null hypothesis is rejected, the sample data does support the hypothesis that there is a negative linear relationship between x and y.

A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected. These data are shown as follows:Total Bill Tip
\$126 \$19
\$58 \$11
\$86 \$20
\$20 \$3
\$59 \$14
\$120 \$30
\$14 \$2
\$17 \$4
\$26 \$2
\$74 \$16

Based upon these data, what is the approximate predicted value for tips if the total bill is \$100?

\$20.61

If the correlation between two variables is known to be statistically significant at the 0.05 level, then the regression slope coefficient will also be significant at the 0.05 level.

True

A perfect correlation between two variables will always produce a correlation coefficient of +1.0

False

A study was recently done in which the following regression output was generated using Excel.

SUMMARY OUTPUT

Given this output, we would reject the null hypothesis that the population regression slope coefficient is equal to zero at the alpha = 0.05 level.True

You are given the following sample data for two variables:

Y X
10 100
8 110
12 90
15 200
16 150
10 100
10 80
8 90
12 150The regression model based on these sample data explains approximately 75 percent of the variation in the dependent variable.

False

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In developing a scatter plot, the decision maker has the option of connecting the points or not.

False

If two variables are spuriously correlated, it means that the correlation coefficient between them is near zero.

False

A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected and the following regression results were observed:

SUMMARY OUTPUTGiven this output, the upper limit for the 95 percent confidence interval estimate for the true regression slope coefficient is approximately 0.28.True

Use the following regression results to answer the question below.

How many observations were involved in this regression?8

If a set of data contains no values of x that are equal to zero, then the regression coefficient, b0, has no particular meaning.

True

A manufacturing company is interested in predicting the number of defects that will be produced each hour on the assembly line. The managers believe that there is a relationship between the defect rate and the production rate per hour. The managers believe that they can use production rate to predict the number of defects. The following data were collected for 10 randomly selected hours.

Defects Production Rate Per Hour
20 400
30 450
10 350
20 375
30 400
25 400
30 450
20 300
10 300
40 300Given these sample data, the simple linear regression model for predicting the number of defects is approximately = 5.67 + 0.048x.True

The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. Given this model, the predicted value for y when x = 40 is 806.2.

True

If two variables are highly correlated, it not only means that they are linearly related, it also means that a change in one variable will cause a change in the other variable.   False

When a correlation is found between a pair of variables, this always means that there is a direct cause and effect relationship between the variables.

False

Ch 14 :
Y is the _____ and X is the ____.

Y = the dependent variable.
X= is the independent variable.

Correlation coefficient

Range 1 to -1
if positive slop is positive
if nagitive slop is nagitive
if 0 then ther is no correlation.
r = sample correlation
r= very close to 0 there is still correlation.
if the r is grater the .7 or lower the -.7 the correlation is strong.
correlation is not the slop if the line.

Ch 14:
hypothesis test

whatever you want to test Is most likely is alternative.
“Test to determent if there is a significant positive correlation.”
p = population correlation coefficient.
Ha p>0
Hn P< or = 0
ANOVA table Null Hypothesis is
B1=0

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regression line

The regression line is in a perfect state of equilibrium.

Residual formula

Residual = Observed – Predicted value.

simple regression analysis

only one X to predict Y

if correlation is there cause and effect?

not always, when a correlation exists between two seemingly unrelated variables, the correlation is said to be a spurious correlation.

Ch 14: Linear Regression
Multiple R

correlation coefficient ( Excel will always give you a positive answer even if it is negative correlation, look at slop to determent if -+)

Ch 14: Linear Regression
R square

(SSR/SST) the amount of variation with in Y, as explained by X. It also says how well our model fits the data. the higher the better the model fits the data.

Ch 14: Linear Regression

has no meaning for liner regression

Ch 14: Linear Regression
standard error

I think it is the average error fore each data point.you times it by 2 and then think to your self is the standard error okay for what i am using my model for.

Ch 14: Linear Regression
equation for the line.

Y^ = b0+b1X
b0= intercept coefficient ( y intercept)
B1 = X vaiable coefficient ( slop)

Ch 14:
What is the domain?

the range form the Max X and min X.

If it is known that a simple linear regression model explains 56 percent of the variation in the dependent variable and that the slope on the regression equation is negative, then we also know that the correlation between x and y is approximately -0.75.

True or FalseTrue

A dependent variable is the variable that we wish to predict or explain in a regression model.

True or FalseTrue

If the correlation between two variables is known to be statistically significant at the 0.05 level, then the regression slope coefficient will also be significant at the 0.05 level.

True or FalseTrue

Both a scatter plot and the correlation coefficient can distinguish between a curvilinear and a linear relationship.

True or FalseFalse

If two variables are spuriously correlated, it means that the correlation coefficient between them is near zero.True or FalseFalsespuriously correlated – is when there is correlation but no causation

Two variables have a correlation coefficient that is very close to zero. This means that there is no relationship between the two variables.

True or FalseFalse

When a correlation is found between a pair of variables, this always means that there is a direct cause and effect relationship between the variables.

True or FalseFalse

A perfect correlation between two variables will always produce a correlation coefficient of +1.0

True or FalseFalse

A correlation of -0.9 indicates a weak linear relationship between the variables.

True or FalseFalse

If a set of data contains no values of x that are equal to zero, then the regression coefficient, b0, has no particular meaning.

True or FalseTrue

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The difference between a scatter plot and a scatter diagram is that the scatter plot has the independent variable on the x-axis while the independent variable is on the Y-axis in a scatter diagram.

True or FalseFalse

In a university statistics course a correlation of -0.8 was found between numbers of classes missed and course grade. This means that the fewer classes students missed, the higher the grade.

Ture or FalseTrue

The scatter plot is a two dimensional graph that is used to graphically represent the relationship between two variables.

Ture or FalseTrue

A research study has stated that the taxes paid by individuals is correlated at a .78 value with the age of the individual. Given this, the scatter plot would show points that would fall on straight line on a slope equal to .78.

True or FalseFalse

When constructing a scatter plot, the dependent variable is placed on the vertical axis and the independent variable is placed on the horizontal axis.

True or False

True

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In developing a scatter plot, the decision maker has the option of connecting the points or not.

True or FalseFalse

If two variables are highly correlated, it not only means that they are linearly related, it also means that a change in one variable will cause a change in the other variable.

True or False ?

False

scatter plot and Scatter diagram

they are the same thing.

Confidence interval

b1+- (t) (b1-standard error)

Which of the following would best describe the situation that a second-degree polynomial regression equation would be used to model?

A parabola

In multiple regression analysis, the model will be developed with one dependent variable and two or more independent variables.

True

(National automotive magazine) Based on this output and your understanding of multiple regression analysis, what is the critical value for testing the significance of the overall regression model at a 0.05 level of statistical significance?

Approximately F = 2.50

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Second-order polynomial models:

Can curve upward or downward depending on the data.

A decision maker has five potential independent variables with which to build a regression model to explain the variation in the dependent variable. At step 1, variable x3 enters the regression model. Which of the following indicates which of the four remaining independent variables will be next to enter the model?

The variable with the highest coefficient of partial determination

(National automotive magazine) Based on this output and your understanding of multiple regression analysis, how many degrees of freedom are associated with the Residual in the ANOVA table?

22

(Yachts) Based on this output, which of the independent variables appear to be significantly helping to predict the price of a yacht, using a 0.10 level of significance?

Age and length

Under what circumstances does the variance inflation factor signal that multicollinearity may be a problem?

When the VIF is greater than or equal to 5

(Yachts) Which of the following statements is correct using the 0.10 level of significance?

Whether or not the yacht has a flying bridge does not significantly affect the price of a yacht, given the other variables present.

(National automotive magazine) Based on this output and your understanding of multiple regression analysis, what percentage of variation in the dependent variable is explained by the regression model?

Approximately 82 percent

(Yachts) Given this information, what percentage of variation in the dependent variable is explained by the regression model?

Approximately 68 percent

In a multiple regression, the dependent variable is house value (in ‘000\$) and one of the independent variables is a dummy variable, which is defined as 1 if a house has a garage and 0 if not. The coefficient of the dummy variable is found to be 5.4 but the t-test reveals that it is not significant at the 0.05 level. Which of the following is true?

The house value remains the same with or without a garage.

The following multiple regression output was generated from a study in which two independent variables are included. The first independent variable (X1) is a quantitative variable measured on a continuous scale. The second variable (X2) is qualitative coded 0 if Yes, 1 if No. Based on this information, which of the following statements is true?

All of the above are true.

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A decision maker is considering including two additional variables into a regression model that has as the dependent variable, Total Sales. The first additional variable is the region of the country (North, South, East, or West) in which the company is located. The second variable is the type of business (Manufacturing, Financial, Information Services, or Other). Given this, how many additional variables will be incorporated into the model?

6

(National automotive magazine) Based on this output and your understanding of multiple regression analysis, which of the following statements is true?

The overall multiple regression model explains a significant portion of the variation in highway mileage when tested at a significance level of 0.05.

(Yachts) Given this information, which is correct regarding the test of the overall model using the 0.10 level of significance?

The overall model has significant ability to predict the price of a yacht because p-value = .001 is less than 0.10

(National automotive magazine) Based on this output and your understanding of multiple regression analysis, what is the adjusted R-square value for this model?

None of the above

In a multiple regression model, which of the following is true?

The sum of the residuals computed for the least squares regression equation will be zero.

If a decision maker wishes to develop a regression model in which the University Class Standing is a categorical variable with 5 possible levels of response, then he will need to include how many dummy variables?

4

(Yachts) Given this information, what is the null hypothesis for testing the overall model?

H0 : β1 = β2 = β3 = β4 = 0

(National automotive magazine) Which of the following might explain why no other independent variables entered the model?

Given the two variables already in the model, none of the others could add significantly to the percentage of variation in the y variable that would be explained by the model.

(National automotive magazine) Based on this output and your understanding of multiple regression analysis, what is the value of the standard error of the estimate for this model?

Approximately 2.02

In a multiple regression analysis involving 15 independent variables and 200 observations, SST = 800 and SSE = 240. The adjusted coefficient of determination is

0.66

Which of the following is NOT considered to be a stepwise regression technique?

Optimal variable entry and removal regression

(Computer magazine) Based on this information, and with a 0.05 level of significance, which of the following conclusions can be justified?

The only significant variable in the model at the .05 level of significance is Hard Drive Capacity.

A regression equation that predicts the price of homes in thousands of dollars is t = 24.6 + 0.055×1 – 3.6×2, where x2 is a dummy variable that represents whether the house in on a busy street or not. Here x2 = 1 means the house is on a busy street and x2 = 0 means it is not. Based on this information, which of the following statements is true?

On average, homes that are on busy streets are worth \$3600 less than homes that are not on busy streets.

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Assume that a time-series plot takes the form of that shown in the following graph: Given this plot, which of the following models would likely give the best fit?

y = b0+ b1t + b1t2+ b1t3

A forecasting model of the following form was developed:
y = B0 + B1xj + B2 + B3 + ε
Which of the following best describes the form of this model?

3rd degree polynomial model

(National automotive magazine) If only one variable were to be brought into the model, which variable should it be if the goal is to explain the highest possible percentage of variation in the dependent variable?

Curb weight

The multiple coefficient of determination measures the percentage of variation in the dependent variable that is explained by the independent variables in the model.

True

A manufacturing company is interested in predicting the number of defects that will be produced each hour on the assembly line. The managers believe that there is a relationship between the defect rate and the production rate per hour. The managers believe that they can use production rate to predict the number of defects. The following data were collected for 10 randomly selected hours. Given these sample data, the simple linear regression model for predicting the number of defects is approximately = 5.67 + 0.048x.

True

An industry study was recently conducted in which the sample correlation between units sold and marketing expenses was 0.57. The sample size for the study included 15 companies. Based on the sample results, test to determine whether there is a significant positive correlation between these two variables. Use an alpha = 0.05

Because t = 2.50 > 1.7709, reject the null hypothesis. There is sufficient evidence to conclude there is a positive linear relationship between sales units and marketing expense for companies in this industry.

If two variables are highly correlated, it not only means that they are linearly related, it also means that a change in one variable will cause a change in the other variable.

False.

The difference between a scatter plot and a scatter diagram is that the scatter plot has the independent variable on the x-axis while the independent variable is on the Y-axis in a scatter diagram.

False.

When a correlation is found between a pair of variables, this always means that there is a direct cause and effect relationship between the variables.

False.

In a university statistics course a correlation of -0.8 was found between numbers of classes missed and course grade. This means that the fewer classes students missed, the higher the grade.

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True.

A dependent variable is the variable that we wish to predict or explain in a regression model.

True.

Both a scatter plot and the correlation coefficient can distinguish between a curvilinear and a linear relationship.

False.

A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected and the following regression results were observed: Given this output, the upper limit for the 95 percent confidence interval estimate for the true regression slope coefficient is approximately 0.28.

If two variables are spuriously correlated, it means that the correlation coefficient between them is near zero.

False.

In a study of 30 customers’ utility bills in which the monthly bill was the dependent variable and the number of square feet in the house is the independent variable, the resulting regression model is = 23.40 + 0.4x. Based on this model, the expected utility bill for a customer with a home with 2,300 square feet is approximately \$92.00.

False.

State University recently randomly sampled ten students and analyzed grade point average (GPA) and number of hours worked off-campus per week. The following data were observed: The correlation between these two variables is approximately -.461

The following regression output is available. Notice that some of the values are missing. Given this information, what percent of the variation in the y variable is explained by the independent variable?

Approximately 57 percent

If a set of data contains no values of x that are equal to zero, then the regression coefficient, b0, has no particular meaning.

True.

When constructing a scatter plot, the dependent variable is placed on the vertical axis and the independent variable is placed on the horizontal axis.

True.

Which of the following is a correct interpretation for the regression slope coefficient?

The average change in y of a one-unit change in x will be b1 units.

If it is known that a simple linear regression model explains 56 percent of the variation in the dependent variable and that the slope on the regression equation is negative, then we also know that the correlation between x and y is approximately -0.75.

True.

If a sample of n = 30 people is selected and the sample correlation between two variables is r = 0.468, what is the test statistic value for testing whether the true population correlation coefficient is equal to zero?

A study was recently done in which the following regression output was generated using Excel. Given this output, we would reject the null hypothesis that the population regression slope coefficient is equal to zero at the alpha = 0.05 level.

True.

A study was recently done in which the following regression output was generated using Excel. Given this, we know that approximately 57 percent of the variation in the y variable is explained by the x variable.

True.

In developing a scatter plot, the decision maker has the option of connecting the points or not.

False.

If the correlation between two variables is known to be statistically significant at the 0.05 level, then the regression slope coefficient will also be significant at the 0.05 level.

FREE Amazon Prime True.

The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. The first observations in the sample for y and x were 300 and 18, respectively. Given this, the residual value for the first observation is approximately 81.6.

False.

A perfect correlation between two variables will always produce a correlation coefficient of +1.0

False.

Two variables have a correlation coefficient that is very close to zero. This means that there is no relationship between the two variables.

False.

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You are given the following sample data for two variables:

Y X
10 100
8 110
12 90
15 200
16 150
10 100
10 80
8 90
12 150The sample correlation coefficient for these data is approximately r = 0.755.True.

you are given the following sample data for two variables:

Y X
10 100
8 110
12 90
15 200
16 150
10 100
10 80
8 90
12 150The regression model based on these sample data explains approximately 75 percent of the variation in the dependent variable.False.

The scatter plot is a two dimensional graph that is used to graphically represent the relationship between two variables.

True

A study was recently performed by the Internal Revenue Service to determine how much tip income waiters and waitresses should make based on the size of the bill at each table. A random sample of bills and resulting tips were collected and the following regression results were observed: Given this output, the point estimate for the average tip per dollar amount of the bill is approximately \$0.21.

True

A research study has stated that the taxes paid by individuals is correlated at a .78 value with the age of the individual. Given this, the scatter plot would show points that would fall on straight line on a slope equal to .78.

False

You are given the following sample data for two variables:

Y X
10 100
8 110
12 90
15 200
16 150
10 100
10 80
8 90
12 150Based upon these sample data, and testing at the 0.05 level of significance, the critical value for testing whether the population correlation coefficient is equal to zero is t = 2.2622.False

Use the following regression results to answer the question below.

How many observations were involved in this regression?8

The following regression model has been computed based on a sample of twenty observations: = 34.2 + 19.3x. Given this model, the predicted value for y when x = 40 is 806.2.

True

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A correlation of -0.9 indicates a weak linear relationship between the variables.

False I hope this helps. I am 100% sure all these answers are correct.

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