### Consider the following partially completed computer printout for a regression analysis Solution

**Consider the following partially completed computer printout for a regression analysis Solution**

1. Consider the following partially completed computer printout for a regression analysis where the dependent variable is the price of a personal computer and the independent variable is the size of the hard drive.

Based on the information provided, what is the F statistic?

About 8 .33

Just over 2.35

About 4.76

About 69.5

4 points

QUESTION 2

1. The standard error of the estimate is a measure of

total variation of the Y variable.

the variation around the sample regression line.

explained variation.

the variation of the X variable.

4 points

QUESTION 3

3.Nintendo Sony would like to test the hypothesis that a difference exists in the average age of users of a Wii, a PlayStation, or an Xbox console game. The following data represent the age of a random sample of Wii, PlayStation, and Xbox users.

Wii PlayStation Xbox

37 26 31

31 21 20

47 24 38

29 24 31

36 25 30

Using α = 0.05, the conclusion for this hypothesis test would be that because the test statistic is

more than the critical value, we cannot conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game.

less than the critical value, we cannot conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game.

more than the critical value, we can conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game.

less than the critical value, we can conclude that there is a difference in the average age of users of a Wii, a PlayStation, or an Xbox console game.

4 points

QUESTION 4

1. The relationship of Y to four other variables was established as Y = 12 + 3X1 - 5X2 + 7X3 + 2X4. When X1 increases 5 units and X2 In a sample of n = 23, the Student's t test statistic for a correlation of r = .500 would be:

2.559

2.819

2.646

can’t say without knowing α (alpha)

4 points

QUESTION 5

1. Given the following ANOVA table (some information is missing), find the F statistic.

3.71

0.99

0.497

4.02

4 points

QUESTION 6

1. Examine the following two-factor analysis of variance table:

Complete the analysis of variance table.

MSA = 40.928, F Factor A =3.35, SSB = 85.35, Factor B df = 3, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 1.8, SSE = 789.29, SSE df = 66, MSE = 12.143

MSA = 40.928, F Factor A = 3.35, SSB = 85.35, Factor B df = 4, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 2.1 SSE = 789.29, SSE df = 66, MSE = 12.143

MSA = 40.698, F Factor A = 3.35, SSB = 84.35, Factor B df = 5, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 2.1, SSE = 789.29, SSE df = 65, MSE = 12.143

MSA = 40.698, F Factor A = 3.35, SSB = 84.35, Factor B df = 3, F Factor B = 2.316, MSAB = 21.859, F Factor AB = 1.8, SSE = 789.29, SSE df = 65, MSE = 12.143

4 points

QUESTION 7

1. The critical value for a two-tailed test of H0: ß1 = 0 at a (alpha) = .05 in a simple regression with 22 observations is:

+ or - 1.725

+ or - 2.086

+ or - 2.528

+ or - 1.960

4 points

QUESTION 8

1. A regression equation that predicts the price of homes in thousands of dollars is t = 24.6 + 0.055x1 - 3.6x2, 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.

On average, homes that are on busy streets are worth $3.6 less than homes that are not on busy streets.

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

On average, homes that are on busy streets are worth $3.6 more than homes that are not on busy streets.

4 points

QUESTION 9

1. The variation attributable to factors other than the relationship between the independent variables and the explained variable in a regression analysis is represented by

regression sum of squares.

error sum of squares.

total sum of squares.

regression mean squares.

4 points

QUESTION 10

1. Degrees of freedom for the between-group variation in a one-factor ANOVA with n1 = 8, n2 = 5, n3 = 7, n4 = 9 would be:

28

3

29

4

4 points

QUESTION 11

1. A hypothesis test is conducted at the 5 percent level of significance to test whether the population correlation is zero. If the sample consists of 25 observations and the correlation coefficient is 0.60, then the computed test statistic would be:

2.071

1.960

3.597

1.645

4 points

QUESTION 12

1. A two-factor analysis of variance is conducted to test the effect that price and advertising have on sales of a particular brand of bottled water. Each week a combination of particular levels of price and advertising are used and the sales amount is recorded. The computer results are shown below.

Based on the results above and a 0.05 level of significance, which of the following is correct?

There is no interaction between price and advertising, so results for individual factors may be misleading.

There is interaction between price and advertising, so the above results for individual factors may be misleading.

There is no interaction between price and advertising, and both factors significantly affect sales.

There is interaction between price and advertising, so the above results conclusively show that both factors affect price.

4 points

QUESTION 13

1. Many companies use well-known celebrities as spokespersons in their TV advertisements. A study was conducted to determine whether brand awareness of female TV viewers and the gender of the spokesperson are independent. Each in a sample of 300 female TV viewers was asked to identify a product advertised by a celebrity spokesperson. The gender of the spokesperson and whether or not the viewer could identify the product was recorded. The numbers in each category are given below.

Male Celebrity Female Celebrity

Identified product 41 61

Could not identify 109 89

Referring to the Table, the degrees of freedom of the test statistic are

1

2

4

299

4 points

QUESTION 14

1. In a multiple regression with six predictors in a sample of 67 U.S. cities, what would be the critical value for an F-test of overall significance at a = .05?

2.29

2.25

2.37

2.18

4 points

QUESTION 15

1. Consider this partially completed one-way ANOVA table:

How many different populations are being considered in this analysis?

2

4

6

5

4 points

QUESTION 16

1. The slope (b1) represents

predicted value of Y when X = 0.

the estimated average change in Y per unit change in X.

the predicted value of Y.

variation around the line of regression.

4 points

QUESTION 17

1. What do we mean when we say that a simple linear regression model is “statistically” useful?

All the statistics computed from the sample make sense.

The model is an excellent predictor of Y.

The model is “practically” useful for predicting Y.

The model is a better predictor of Y than the sample mean, .

4 points

QUESTION 18

1. Nintendo Sony would like to test the hypothesis that a difference exists in the average age of users of a Wii, a PlayStation, or an Xbox console game. The following data represent the age of a random sample of Wii, PlayStation, and Xbox users.

Wii PlayStation Xbox

37 26 31

31 21 20

47 24 38

29 24 31

36 25 30

Using α = 0.05, the critical value for this hypothesis test would be ________.

3.885

4.581

5.718

6.040

4 points

QUESTION 19

1. The following regression output was generated based on a sample of utility customers. The dependent variable was the dollar amount of the monthly bill and the independent variable was the size of the house in square feet.

Based on this regression output, which of the following statements is not true?

The number of square feet in the house explains only about 2 percent of the variation in the monthly power bill.

At an alpha level equal to 0.05, there is no basis for rejecting the hypothesis that the slope coefficient is equal to zero.

The average increase in the monthly power bill is about 66.4 for each additional square foot of space in the house.

The correlation of the monthly power bill with the square footage of the house is 0.149

4 points

QUESTION 20

1. Consider this partially completed one-way ANOVA table:

Based on the analysis of variance F-test, what conclusion should be reached regarding the null hypothesis? Test using alpha = 0.05.

Since 11.1309 > 2.9467 accept H0 and conclude that all population means are the same.

Since 2.9467 > 11.1309 accept H0 and conclude that all population means are the same.

Since 11.1309 > 2.9467 reject H0 and conclude that at least two populations means are different.

Since 2.9467 > 11.1309 reject H0 and conclude that at least two populations means are different.

4 points

QUESTION 21

1. The following EXCEL tables are obtained when "Score received on an exam (measured in percentage points)" (Y) is regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course.

Regression Statistics

Multiple R 0.142620229

R Square 0.02034053

Adjusted R Square -0.028642444

Standard Error 20.25979924

Observations 22

Coefficients Standard Error T Stat P-value

Intercept 39.39027309 37.24347659 1.057642216 0.302826622

Attendance 0.340583573 0.52852452 0.644404489 0.526635689

Which of the following statements is true?

If attendance increases by 0.341%, the estimated average score received will increase by 1 percentage point.

If attendance increases by 1%, the estimated average score received will increase by 39.39 percentage points.

If attendance increases by 1%, the estimated average score received will increase by 0.341 percentage points.

If the score received increases by 39.39%, the estimated average attendance will go up by 1%.

4 points

QUESTION 22

1. A local trucking company fitted a regression to relate the travel time (days) of its shipments as a function of the distance traveled (miles). The fitted regression is Time = -7.126 + .0214 Distance, based on a sample of 20 shipments. The estimated standard error of the slope is 0.0053. Find the critical value for a right-tailed test to see if the slope is positive, using a (alpha) = .05.

2.101

2.552

1.960

1.734

4 points

QUESTION 23

1. The following regression output is from a multiple regression model:

The variables t, t2, and t3 represent the t, t-squared, and t-cubed respectively where t is the indicator of time from periods t = 1 to t = 20. Which of the following best describes the type of forecasting model that has been developed?

A complete third-order polynomial model

A tri-variate smoothed regression model

A nonlinear trend model

A qualitative regression model

4 points

QUESTION 24

1. Examine the following two-factor analysis of variance table:

Does the ANOVA table indicate that the levels of factor B have equal means? Use a significance level of 0.05.

Fail to reject H0. Conclude that there is not sufficient evidence to indicate that at least two levels of Factor B have different mean responses.

Reject H0. Conclude that there is sufficient evidence to indicate that at least two levels of Factor B have different mean responses.

Fail to reject H0. Conclude that there is sufficient evidence to indicate that at least two levels of Factor B have different mean responses.

Reject H0. Conclude that there is not sufficient evidence to indicate that at least two levels of Factor B have different mean responses.

4 points

QUESTION 25

1. Parents complain that children read too few storybooks and watch too much television nowadays. A survey of 1,000 children reveals the following information on average time spent watching TV and average time spent reading storybooks

Average time spent reading story books

Average time spent watching TV Less than 1 hour Between 1and 2 hours More than 2 hours

Less than 2 hours 90 85 130

More than 2 hours 655 32 8

Referring to the Table, if the null hypothesis of no connection between time spent watching TV and time spent reading story books is true, how many children watching less than 2 hours of TV and reading no more than 2 hours of story books on average can we expect?

35.69

227.23

262.91

969.75

4 points

QUESTION 26

1. With two-way ANOVA, the total sum of squares is portioned in the sum of squares for

Factor A, Factor B, block, and error.

Factor A, Factor B, within, and error.

Factor A, Factor B, interaction, and error.

Factor A, Factor B, interaction, and between.

4 points

QUESTION 27

1. Consider this partially completed one-way ANOVA table:

Fill in the ANOVA table with the missing values.

SSB = 483, MSB = 161, F-ratio = 11.1309, Within Samples df = 28, MSW = 14.464

SSB = 483, MSB = 161, F- ratio = 8.1629, Within Samples df = 28, MSW = 14.464

SSB = 483, MSB = 161, F-ratio = 8.1629, Within Samples df = 25, MSW = 14.464

SSB = 504, MSB = 161, F-ratio = 8.1629, Within Samples df = 28, MSW = 14.464

4 points

QUESTION 28

1. ________ ANOVA relies on matched samples in a similar way to the matched-pairs hypothesis testing that compares two population means.

One-way

Randomized block

Two-way

Three-way

4 points

QUESTION 29

1. The following EXCEL tables are obtained when "Score received on an exam (measured in percentage points)" (Y) is regressed on "percentage attendance" (X) for 22 students in a Statistics for Business and Economics course.

Regression Statistics

Multiple R 0.142620229

R Square 0.02034053

Adjusted R Square -0.028642444

Standard Error 20.25979924

Observations 22

Coefficients Standard Error T Stat P-value

Intercept 39.39027309 37.24347659 1.057642216 0.302826622

Attendance 0.340583573 0.52852452 0.644404489 0.526635689

2.

Which of the following statements is true?

-2.86% of the total variability in score received can be explained by percentage attendance.

-2.86% of the total variability in percentage attendance can be explained by score received.

2% of the total variability in score received can be explained by percentage attendance.

2% of the total variability in percentage attendance can be explained by score received.

4 points

QUESTION 30

1. In a particular model, the sum of the squared residuals was 847. If the model had 5 independent variables, and the data set contained 40 points, the value of the standard error of the estimate is 24.911.

True

False

4 points

QUESTION 31

1. 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?

The model explains nearly 63 percent of the variation in the dependent variable

If tested at the 0.05 significance level, the overall model would be considered statistically significant.

The variable X1 has a slope coefficient that is significantly different from zero if tested at the 0.05 level of significance.

All of the above are true.

4 points

QUESTION 32

The ________ is another term for the variance of the sample data.

mean square total

mean square between

mean square within

total sum of squares

4 points

QUESTION 33

1. We are interested in determining whether the opinions of the individuals on gun control (as to Yes, No, and No Opinion) are uniformly distributed. A sample of 150 was taken and the following data were obtained.

The conclusion of the test with alpha = 0.05 is that the views of people on gun control are:

uniformly distributed.

not uniformly distributed.

inconclusive.

None of the above

4 points

QUESTION 34

1. When testing for independence in a contingency table with 3 rows and 4 columns, there are ________ degrees of freedom.

5

6

7

12

4 points

QUESTION 35

1. The following regression output was generated based on a sample of utility customers. The dependent variable was the dollar amount of the monthly bill and the independent variable was the size of the house in square feet.

Based on this regression output, what is the 95 percent confidence interval estimate for the population regression slope coefficient?

Approximately -0.0003 ----- +0.0103

About -0.0082 ----- +0.0188

Approximately -32.76 ----- +32.79

None of the above

4 points

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