Questions have been revised accordingly Please kindly review the questions below, thank you 1 A test is conducted in 22 cities to see if giving away free transit system maps will increase the number of bus riders In a regression analysis, the dependent variable Y is the increase in bus riders (in thousands of persons) from the start of the test until its conclusion The independent variables are X 1 the number (in thousands) of free maps distributed and a binary variable X 2 1 if the city has free downtown parking, 0 otherwise The estimated regression equation is Y 1 32 0 0345 X 1 1 45 X 2 In city 3, the observed Y value is 7 3, X 1 140, and X 2 0 The residual for city 3 (in thousands) is a 6 15 b 1 15 c 4 83 d 1 57 2 Mary used a sample of 68 large U S cities to estimate the relationship between Crime (annual property crimes per 100,000 persons) and Income (median annual income per capita, in dollars) Her estimated regression equation was Crime 428 0 050 Income If Income decreases by 1000, we would expect that Crime will a increase by 428 b decrease by 50 c increase by 500 d remain unchanged 3 A predictor that is significant in a one tailed t test will also be significant in a two tailed test at the same level of significance Select one True False 4 A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function of Size (measured in thousands of square feet) and whether or not there is a fireplace ( FP is 0 if there is no fireplace, 1 if there is a fireplace) Part of the regression output is provided below, based on a sample of 20 homes Some of the information has been omitted Variable Coefficients Standard Error t Statistic P value Intercept 128 93746 2 6205302 49 203 8 93E 20 Size 1 2072436 11 439 2 09E 09 FP 6 47601954 1 9803612 3 27 0 004512 Which statement is supported by the regression output a At 05, FP is not a significant predictor in a two tailed test b A fireplace adds around $6,476 to the selling price of the average house c A large house with no fireplace will sell for more than a small house with a fireplace d FP is a more significant predictor than Size 5 A negative correlation between two variables X and Y usually yields a negative p value for r Select one True False 6 A news network stated that a study had found a positive correlation between the number of children a worker has and his or her earnings last year You may conclude that a people should have more children so they can get better jobs b the data are erroneous because the correlation should be negative c correlation does not demonstrate causation d statisticians have small families 7 Multicollinearity can be detected from t tests of the predictor variables Select one True False 9 In a sample of n 36, the Student's t test statistic for a correlation of r 450 would be a 2 110 b 2 938 c 2 030 d impossible to calculate without knowing 10 In a regression with 7 predictors and 62 observations, degrees of freedom for a t test for each coefficient would use how many degrees of freedom a 61 b 60 c 55 d 54 11 Which statement is not correct a Spurious correlation can often be reduced by expressing X and Y in per capita terms b Autocorrelation is mainly a concern when we are using time series data c Heteroscedastic residuals will have roughly the same variance for any value of X d Standardized residuals make it easy to identify outliers or instances of poor fit 12 In a multiple regression with five predictors in a sample of 56 U S cities, what would be the critical value for an F test of overall significance at 05 a 2 45 b 2 37 c 2 40 d 2 56 13 A sample correlation r 40 indicates a stronger linear relationship than r 60 Select one True False 14 Confidence intervals for predicted Y are less precise when the residuals are very small Select one True False 15 In a multiple regression with five predictors in a sample of 56 U S cities, we would use F 5,50 in a test of overall significance Select one True False 16 If the residuals violate the assumption of normality, we expect that a the sample was not taken randomly b the residuals will not sum to zero c least squares formulas will fail d confidence intervals may be unreliable 17 Simple tests for nonlinearity in a regression model can be performed by a squaring the standard error b including squared predictors c deleting predictors one at a time d multiplying two predictors 18 Find the slope of the simple regression of Y on X X Y 3 9 5 13 9 10 13 23 15 35 a 2 595 b 1 109 c 2 221 d 1 884 19 In a multiple regression, which is an incorrect statement about the residuals a They may be used to test for multicollinearity b They are differences between observed and estimated values of Y c Their sum will always equal zero d They may be used to detect heteroscedasticity 20 When comparing the 90 percent prediction and confidence intervals for a given regression analysis a the prediction interval is narrower than the confidence interval b the prediction interval is wider than the confidence interval c there is no difference between the size of the prediction and confidence intervals d no generalization is possible about their comparative width 21 If the attendance at a baseball game is to be predicted by the equation Attendance 16,500 75 Temperature , what would be the predicted attendance if Temperature is 90 degrees a 6,750 b 9,750 c 12,250 d 10,020 22 In the following regression, which are the three best predictors Variables Coefficients Standard Error t (df 81) p value Intercept 9 8080 16 9900 0 577 5654 NumCyl 1 6804 0 5757 2 919 0045 HPMax 0 0369 0 0140 2 630 0102 ManTran 0 2868 1 2802 0 224 8233 Length 0 1109 0 0601 1 845 0686 Wheelbase 0 0701 0 1714 0 409 6836 Width 0 4079 0 2922 1 396 1665 RearStRm 0 0085 0 2018 0 042 9666 Weight 0 0025 0 0020 1 266 2090 Domestic 1 2291 1 1391 1 079 2838 a ManTran , Wheelbase , RearStRm b ManTran , Length , Width c NumCyl , HPMax , Length d Cannot be ascertained from the given information 23 Confidence intervals for Y may be unreliable when the residuals are not normally distributed Select one True False 24 Using a two tailed test at 05 for n 30, we would reject the hypothesis of zero correlation if the absolute value of r exceeds a 2992 b 3609 c 0250 d 2004 25 Based on the following regression ANOVA table, what is the MS for the residuals Source df SS MS F Regression 4 1793 2356 448 3089 7 48540 Residual 45 2695 0996 Total 49 4488 3352 a 2695 0996 b 59 8911 c 673 7749 d insufficient information to answer 26 In a sample of n 20, the critical value of the correlation coefficient for a two tailed test at 05 is a 587 b 412 c 444 d 497 27 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 0 0214 Distance , based on a sample of 20 shipments The estimated standard error of the slope is 0 0053 Find the value of t calc to test for zero slope a 2 46 b 5 02 c 4 04 d 3 15 28 Which is a characteristic of the variance inflation factor (VIF) a It is insignificant unless the corresponding t statistic is significant b It reveals collinearity rather than multicollinearity c It measures the degree of significance of each predictor d It indicates the predictor's degree of multicollinearity 29 If there is no significant correlation between the response and explanatory variables then the slope of the regression line would be a positive b negative c zero d unknown 30 In a sample of n 23, the critical value of the correlation coefficient for a two tailed test at 05 is a 524 b 412 c 500 d 497 31 Based on these regression results, in your judgment which statement is most nearly correct ( Y highway miles per gallon in 91 cars) R 2 0 499 Adjusted R 2 0 444 n 91 R 0 707 k 9 Standard Error 4 019 Dependent Variable HwyMPG Source SS df MS F p value Regression 1,305 7251 9 145 0806 8 98 0000 Residual 1,308 3848 81 16 1529 Total 2,614 1099 90 a The number of predictors is rather small b Some predictors are not contributing much c Prediction intervals would be fairly narrow in terms of MPG d The overall model lacks significance and or predictive power 32 A researcher's results are shown below using Femlab (labor force participation rate among females) to try to predict Cancer (death rate per 100,000 population due to cancer) in the 50 U S states Source of variation df SS MS F Regression 1 5377 836 5377 836 5 228879 Residual 48 49367 389 1028 487 Total 49 54745 225 What is the R 2 for this regression a 9018 b 0982 c 8395 d 1605 33 A parsimonious model is one with many weak predictors but a few strong ones Select one True False

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Questions have been revised accordingly. Please kindly review the questions below, thank you. 1 A test is conducted in 22 cities to see if giving

Questions have been revised accordingly.

Please kindly review the questions below, thank you.

A test is conducted in 22 cities to see if giving away free transit system maps will increase the number of bus riders. In a regression analysis, the dependent variableYis the increase in bus riders (in thousands of persons) from the start of the test until its conclusion. The independent variables areX₁= the number (in thousands) of free maps distributed and a binary variableX₂= 1 if the city has free downtown parking, 0 otherwise. The estimated regression equation isY= 1.32 + 0.0345X₁ 1.45X₂. In city 3, the observedYvalue is 7.3,X₁= 140, andX₂= 0. The residual for city 3 (in thousands) is

6.15

1.15

4.83

1.57

Mary used a sample of 68 large U.S. cities to estimate the relationship betweenCrime(annual property crimes per 100,000 persons) andIncome(median annual income per capita, in dollars). Her estimated regression equation wasCrime= 428 + 0.050Income.IfIncomedecreases by 1000, we would expect thatCrimewill

increase by 428.

decrease by 50.

increase by 500.

remain unchanged.

A predictor that is significant in a one-tailedt-test will also be significant in a two-tailed test at the same level of significance.

Select one:

True

False

A realtor is trying to predict the selling price of houses in Greenville (in thousands of dollars) as a function ofSize(measured in thousands of square feet) and whether or not there is a fireplace (FPis 0 if there is no fireplace, 1 if there is a fireplace). Part of the regression output is provided below, based on a sample of 20 homes. Some of the information has been omitted.

Variable	Coefficients	Standard Error	t-Statistic	P-value
Intercept	128.93746	2.6205302	49.203	8.93E-20
Size		1.2072436	11.439	2.09E-09
FP	6.47601954	1.9803612	3.27	0.004512

Which statement is supported by the regression output?

At= .05,FPis not a significant predictor in a two-tailed test.

A fireplace adds around $6,476 to the selling price of the average house.

A large house with no fireplace will sell for more than a small house with a fireplace.

FPis a more significant predictor thanSize.

A negative correlation between two variablesXandYusually yields a negativep-value forr.

Select one:

True

False

A news network stated that a study had found a positive correlation between the number of children a worker has and his or her earnings last year. You may conclude that

people should have more children so they can get better jobs.

the data are erroneous because the correlation should be negative.

correlation does not demonstrate causation.

statisticians have small families.

Multicollinearity can be detected fromttests of the predictor variables.

Select one:

True

False

In a sample ofn= 36, the Student'sttest statistic for a correlation ofr= .450 would be

2.110.

2.938.

2.030.

impossible to calculate without knowing.

In a regression with 7 predictors and 62 observations, degrees of freedom for attest for each coefficient would use how many degrees of freedom?

Which statement isnotcorrect?

Spurious correlation can often be reduced by expressingXandYin per capita terms.

Autocorrelation is mainly a concern when we are using time-series data.

Heteroscedastic residuals will have roughly the same variance for any value ofX.

Standardized residuals make it easy to identify outliers or instances of poor fit.

In a multiple regression with five predictors in a sample of 56 U.S. cities, what would be the critical value for anFtest of overall significance at= .05?

2.45

2.37

2.40

2.56

A sample correlationr= .40 indicates a stronger linear relationship thanr= .60.

Select one:

True

False

Confidence intervals for predictedYare less precise when the residuals are very small.

Select one:

True

False

In a multiple regression with five predictors in a sample of 56 U.S. cities, we would useF_5,50in a test of overall significance.

Select one:

True

False

If the residuals violate the assumption of normality, we expect that

the sample was not taken randomly.

the residuals will not sum to zero.

least squares formulas will fail.

confidence intervals may be unreliable.

Simple tests for nonlinearity in a regression model can be performed by

squaring the standard error.

including squared predictors.

deleting predictors one at a time.

multiplying two predictors.

Find the slope of the simple regression ofYonX.

X	Y
3	9
5	13
9	10
13	23
15	35

2.595

1.109

2.221

1.884

In a multiple regression, which is anincorrectstatement about the residuals?

They may be used to test for multicollinearity.

They are differences between observed and estimated values ofY.

Their sum will always equal zero.

They may be used to detect heteroscedasticity.

When comparing the 90 percent prediction and confidence intervals for a given regression analysis

the prediction interval is narrower than the confidence interval.

the prediction interval is wider than the confidence interval.

there is no difference between the size of the prediction and confidence intervals.

no generalization is possible about their comparative width.

If the attendance at a baseball game is to be predicted by the equationAttendance= 16,500 75Temperature, what would be the predicted attendance ifTemperatureis 90 degrees?

6,750

9,750

12,250

10,020

In the following regression, which are the threebestpredictors?

Variables	Coefficients	Standard Error	t (df = 81)	p-value
Intercept	9.8080	16.9900	0.577	.5654
NumCyl	1.6804	0.5757	2.919	.0045
HPMax	0.0369	0.0140	2.630	.0102
ManTran	0.2868	1.2802	0.224	.8233
Length	0.1109	0.0601	1.845	.0686
Wheelbase	0.0701	0.1714	0.409	.6836
Width	0.4079	0.2922	1.396	.1665
RearStRm	0.0085	0.2018	0.042	.9666
Weight	0.0025	0.0020	1.266	.2090
Domestic	1.2291	1.1391	1.079	.2838

ManTran,Wheelbase,RearStRm

ManTran,Length,Width

NumCyl,HPMax,Length

Cannot be ascertained from the given information

Confidence intervals forYmay be unreliable when the residuals are not normally distributed.

Select one:

True

False

Using a two-tailed test at= .05 forn= 30, we would reject the hypothesis of zero correlation if the absolute value ofrexceeds

.2992.

.3609.

.0250.

.2004.

Based on the following regression ANOVA table, what is theMSfor the residuals?

Source	df	SS	MS	F
Regression	4	1793.2356	448.3089	7.48540
Residual	45	2695.0996
Total	49	4488.3352

2695.0996

59.8911

673.7749

insufficient information to answer

In a sample ofn= 20, the critical value of the correlation coefficient for a two-tailed test at= .05 is

.587.

.412.

.444.

.497.

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 isTime= 7.126 + 0.0214Distance, based on a sample of 20 shipments. The estimated standard error of the slope is 0.0053. Find the value oft_calcto test for zero slope.

2.46

5.02

4.04

3.15

Which is a characteristic of the variance inflation factor (VIF)?

It is insignificant unless the correspondingtstatistic is significant.

It reveals collinearity rather than multicollinearity.

It measures the degree of significance of each predictor.

It indicates the predictor's degree of multicollinearity.

If there is no significant correlation between the response and explanatory variables then the slope of the regression line would be

positive.

negative.

zero.

unknown.

In a sample ofn= 23, the critical value of the correlation coefficient for a two-tailed test at= .05 is

.524.

.412.

.500.

.497.

Based on these regression results, in your judgment which statement is most nearly correct (Y= highway miles per gallon in 91 cars)?

R²	0.499
Adjusted R²	0.444	n	91
R	0.707	k	9
Standard Error	4.019	Dependent Variable	HwyMPG

Source	SS	df	MS	F	p-value
Regression	1,305.7251	9	145.0806	8.98	.0000
Residual	1,308.3848	81	16.1529
Total	2,614.1099	90

The number of predictors is rather small.

Some predictors are not contributing much.

Prediction intervals would be fairly narrow in terms of MPG.

The overall model lacks significance and/or predictive power.

A researcher's results are shown below usingFemlab(labor force participation rate among females) to try to predictCancer(death rate per 100,000 population due to cancer) in the 50 U.S. states.