ISDS COPE FINAL

Calculate the value of R2 given the ANOVA portion of the following regression output: Source of variance SS df MS F p-value Regression 2,562 1. 2,562 6.58. 0.0145 Residual 14,395. 37. 389 Total 16,957 38 A. 0.151 B. 0.515 C. 0.849 D. 1.000

A. 0.151

The accompanying table shows the regression results when estimating y = β0 + β1x + ε. Coefficients Standard Error t-stat p-value Intercept 0.083. 3.56 0.9822 x 1.417 0.63 0.0745 When testing whether the slope coefficient differs from 1, the value of the test statistic is A. 0.66 B. 1.42 C. 1.96 D. 2.25

A. 0.66

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether x significantly influences y, the null hypothesis takes the form ______________. A. H0:β1 = 0 B. H0:β1 = 1 C. H0:b1 = 0 D. H0:b1 = 1

A. H0:β1 = 0

Using the same data set, four models are estimated using the same response variable, however, the number of explanatory variables differs. Which of the following models provides the best fit? Model 1. Model 2 Model 3. Model 4 Multiple R 0.993. 0.991 0.936. 0.746 R Square. 0.987. 0.982. 0.877 0.557 Adjusted R 0.982 0.978 0.849 0.513 Standard Er 4,043 4,463 11,615 20,878 Observations 12 12 12 12 A. Model 1 B. Model 2 C. Model 3 D. Model 4

A. Model 1

Given the following portion of regression results, which of the following conclusions is true with regard to the F test at the 5% significance level? df SS MS F Significance F Regression 2 3,500. 1,750 0.1000 Residual 20 13,500. 675 Total. 22. 17,000 A. Neither of the explanatory variables is significantly related to the response variable. B. Both of the explanatory variables are significantly related to the response variable. C. Exactly one of the explanatory variables is significantly related to the response variable. D. At least one of the explanatory variables is significantly related to the response variable.

A. Neither of the explanatory variables is significantly related to the response variable.

A researcher studies the relationship between SAT scores, the test-taker's family income, and his or her grade point average (GPA). Data are collected from 24 students. He estimates the following model: SAT = β0 + β1 GPA + β2 Income + ε. The following table summarizes a portion of the regression results. df SS MS. F Regression. 2 141,927.9571 70,963.98 Residual. 21 22,167.8762 1,055.613 Total 23 164.095.8333 Coefficients Standard Error. t-stat. p-value Intercept 1,104.2580 54.7524. 20.1682 0.0000 GPA 150.9920 15.0931. 10.0040 0.0000 Income 0.0017. 0.0003. 6.7696 0.0000 At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant? A. Only Income. B. Both, GPA and Income. C. Only GPA. D. Neither GPA nor Income.

A. Only Income.

Tukey's honestly significant differences (HSD) method ensures that the probability of a Type I error remains fixed irrespective of the number of ________________. A. pairwise comparisons B. treatments C. replications within each treatment D. replications for each combination of factor A and factor B

A. pairwise comparisons

Refer to the portion of regression results in the accompanying table. df SS MS. F. Significance F Regression 2 7,562. 3,781 0.0028 Residual 20 9,395 470 Total 22. 16,957 When testing the overall significance of the regression model at the 5% level given a critical value of F0.05,(2.20) = 3.49, the decision is to A. reject H0 and conclude that the explanatory variables are jointly significant. B. not reject H0 and conclude that the explanatory variables are jointly significant. C. reject H0 and conclude that the explanatory variables are not jointly significant. D. not reject H0 and conclude that the explanatory variables are not jointly significant.

A. reject H0 and conclude that the explanatory variables are jointly significant.

Simple linear regression analysis differs from multiple regression analysis in that A. simple linear regression uses only one explanatory variable B. the coefficient of correlation is meaningless in simple linear regression C. goodness-of-fit measures cannot be calculated with simple linear regression D. the coefficient of determination is always higher in simple linear regression

A. simple linear regression uses only one explanatory variable

In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, which of the following is the standard error of the estimate? A. -1 B. 0 C. +1 D. Infinity

B. 0

Given the following portion of regression results, which of the following is the value of the F(2,20) test statistic? df SS MS F Significance F Regression 2 3,500. 1,750 0.1000 Residual 20 13,500. 675 Total. 22. 17,000 A. 1.96 B. 2.59 C. 3.49 D. 10

B. 2.59

Fisher's LSD method is applied when the A. ANOVA test has not rejected the null hypothesis of equal population means. B. ANOVA test has rejected the null hypothesis of equal population means. C. two-sample t test is not applicable. D. None of these choices is correct.

B. ANOVA test has rejected the null hypothesis of equal population means.

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a one-to-one relationship between x and y, the null hypothesis takes the form ______________. A. H0:β1 = 0 B. H0:β1 = 1 C. H0:b1 = 0 D. H0:b1 = 1

B. H0:β1 = 1

A researcher studies the relationship between SAT scores, the test-taker's family income, and his or her grade point average (GPA). Data are collected from 24 students. He estimates the following model: SAT = β0 + β1 GPA + β2 Income + ε. The following table summarizes a portion of the regression results. df SS MS. F Regression. 2 141,927.9571 70,963.98 Residual. 21 22,167.8762 1,055.613 Total 23 164.095.8333 Coefficients Standard Error. t-stat. p-value Intercept 1,104.2580 54.7524. 20.1682 0.0000 GPA 150.9920 15.0931. 10.0040 0.0000 Income 0.0017. 0.0003. 6.7696 0.0000 Which of the following is the correct hypotheses for testing the joint significance? A. H0:β0 = β2 = 0; HA: At least β0 ≠ 0 B. H0:β1 = β2 = 0; HA: At least one βj ≠ 0 C. H0:β0 = β1 = β2 = 0; HA: All βj ≠ 0 D. H0:β1 = β2 = 0; HA: Both βj ≠ 0

B. H0:β1 = β2 = 0; HA: At least one βj ≠ 0

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a positive linear relationship between x and y, the alternative hypothesis takes the form ______________. A. HA:β1 = 0 B. HA:β1 > 1 C. HA:β1 < 0 D. HA:b1 > 1

B. HA:β1 > 1

The accompanying table shows the regression results when estimating y = β0 + β1x + ε. Coefficients Standard Error t-stat p-value Intercept 0.083. 3.56 0.02 0.9822 x 1.417 0.63 2.25 0.0745 Is x significantly related to y at the 5% significance level? A. Yes, because the p-value of 0.0745 is greater than 0.05. B. No, because the p-value of 0.0745 is greater than 0.05. C. Yes, because the slope coefficient of 1.417 is less than the test statistic of 2.25. D. No, because the slope coefficient of 1.417 is less than the test statistic of 2.25.

B. No, because the p-value of 0.0745 is greater than 0.05.

When confronted with multicollinearity, a good remedy is to _______________________ if we can justify its redundancy. A. add one more collinear variable B. drop one of the collinear variables C. remove both the collinear variables D. add as many collinear variables as possible

B. drop one of the collinear variables

When using Fisher's LSD method at some stated significance level, the probability of committing a Type I error increases as the number of _________________________. A. pairwise comparisons decreases B. pairwise comparisons increases C. sample size increases D. treatments decreases

B. pairwise comparisons increases

In a simple linear regression model, if the plots on a scatter diagram lie on a straight line, which of the following is the coefficient of determination? A. -1 B. 0 C. +1 D. Infinity

C. +1

When estimating = β0 + β1x1 + β2x2 +ε, the following regression results using ANOVA were obtained. df SS MS. F Regression 2 210.9 105.5. 114.7 Residual 17. 15.6 0.92 Total. 19 226.5 Coefficients Standard Error t-stat p-value Intercept −1.6 0.57 −2.77 0.0132 x1 −0.5. 0.04. −15.11 2.77E-11 x2 0.1 0.07. 1.89. 0.0753 Which of the following is the adjusted R2? A. 0.82 B. 0.86 C. 0.92 D. 0.96

C. 0.92

A researcher studies the relationship between SAT scores, the test-taker's family income, and his or her grade point average (GPA). Data are collected from 24 students. He estimates the following model:SAT = β0 + β1 GPA + β2 Income + ε. The following table summarizes a portion of the regression results. df SS MS. F Regression. 2 141,927.9571 70,963.98 Residual. 21 22,167.8762 1,055.613 Total 23 164.095.8333 Coefficients Standard Error. t-stat. p-value Intercept 1,104.2580 54.7524. 20.1682 0.0000 GPA 150.9920 15.0931. 10.0040 0.0000 Income 0.0017. 0.0003. 6.7696 0.0000 Which of the following is the value of the test statistic for testing the joint significance of the linear regression model? A. 6.40 B. 134.45 C. 67.23 D. 45.13

C. 67.23

Given the following portion of regression results, which of the following is the value of the F2,20 test statistic? df SS MS. F. Significance F Regression 2 7,562. 3,781 0.0028 Residual 20 9,395 470 Total 22. 16,957 A. 1.96 B. 3.49 C. 8.04 D. 10

C. 8.04

Consider the sample regression equation = 12 + 3x1 - 5x2 + 7x3 - 2x4. When x1 increases by 1 unit and x2 increases by 2 units, while x3 and x4 remain unchanged, what change would you expect in the predicted y? A. Decrease by 2 B. Decrease by 4 C. Decrease by 7 D. No change in predicted y

C. Decrease by 7

Consider the following simple linear regression model: y = β0 + β1x + ε. When determining whether there is a negative linear relationship between x and y, the alternative hypothesis takes the form ______________. A. HA:β1 = 0 B. HA:β1 > 0 C. HA:b1 < 0 D. HA:b1 > 0

C. HA:b1 < 0

Consider the following sample regression equation = 150 - 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). If the price of the good increases by $3, then we expect demand for Product A to ______________. A. increase by 60 B. decrease by 60 C. decrease by 60,000 D. increase by 60,000

C. decrease by 60,000

In regression, multicollinearity is considered problematic when two or more explanatory variables are ___________. A. not correlated B. rarely correlated C. highly correlated D. moderately correlated

C. highly correlated

If the interaction between two factors is not significant, the next tests to be done are ___________________. A. none, the analysis is complete B. none, gather more data C. tests about the population means of factor A or factor B using two-way ANOVA without interaction D. Tukey's confidence intervals

C. tests about the population means of factor A or factor B using two-way ANOVA without interaction

Consider the following sample regression equation = 150 - 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). The slope coefficient indicates that if ______________. A. the price of Product A increases by $1, then on average, demand decreases by 20 B. the price of Product A increases by $1, then on average, demand increases by 20 C. the price of Product A increases by $1, then on average, demand decreases by 20,000 D. the price of Product A increases by $1, then on average, demand increases by 20,000

C. the price of Product A increases by $1, then on average, demand decreases by 20,000

The standard error of the estimate measures ____________. A. the variability of the explanatory variables. B. the variability of the values of the sample regression coefficients. C. the variability of the observed y-values around the predicted y-values. D. the variability of the predicted y-values around the mean of the observed y-values.

C. the variability of the observed y-values around the predicted y-values.

The accompanying table shows the regression results when estimating y = β0 + β1x1 + β2x2 + β3x3 + ε. df SS MS F Significance F Regression 3 453 151. 5.03 0.0030 Residual 85 2,521 30 Total 88 2,974 Coefficients Standard Error t-stat p-value Intercept. 14.96 3.08 4.80 0.0000 x1 0.87 0.29 3.00 0.0035 x2 0.46 0.22 2.09. 0.0400 x3 0.04 0.34. 0.12 0.9066 At the 5% significance level, which of the following explanatory variable(s) is(are) individually significant? A. Only x1 B. Only x3 C. x1 and x2 D. x2 and x3

C. x1 and x2

When estimating = β0 + β1x1 + β2x2 +ε, the following regression results using ANOVA were obtained. df SS MS. F Regression 2 210.9 105.5. 114.7 Residual 17. 15.6 0.92 Total. 19 226.5 Coefficients Standard Error t-stat p-value Intercept −1.6 0.57 −2.77 0.0132 x1 −0.5. 0.04. −15.11 2.77E-11 x2 0.1 0.07. 1.89. 0.0753 Which of the following is the coefficient of determination? A. 0.07 B. 0.10 C. 0.90 D. 0.93

D. 0.93

When estimating = β0 + β1x1 + β2x2 +ε, the following regression results using ANOVA were obtained. df SS MS. F Regression 2 210.9 105.5. 114.7 Residual 17. 15.6 0.92 Total. 19 226.5 Coefficients Standard Error t-stat p-value Intercept −1.6 0.57 −2.77 0.0132 x1 −0.5. 0.04. −15.11 2.77E-11 x2 0.1 0.07. 1.89. 0.0753 Which of the following is the standard error of the estimate? A. 0.82 B. 0.86 C. 0.92 D. 0.96

D. 0.96

The accompanying table shows the regression results when estimating y = β0 + β1x + ε. Coefficients Standard Error t-stat p-value Intercept 0.083. 3.56 0.9822 x 1.417 0.63 0.0745 Which of the following is the value of the test statistic when testing whether x significantly influences y? A. 0.66 B. 1.42 C. 1.96 D. 2.25

D. 2.25

Consider the following sample regression equation = 150 - 20x, where y is the demand for Product A (in 1,000s) and x is the price of the product (in $). If the price of Product A is $5, then we expect demand to be ______. A. 50 B. 500 C. 5,000 D. 50,000

D. 50,000

Given the following portion of regression results, which of the following conclusions is true with regard to the F test at the 5% significance level? df SS MS. F. Significance F Regression 2 7,562. 3,781 8.04 0.0028 Residual 20 9,395 470 Total 22. 16,957 A. Neither of the explanatory variables is related to the response variable. B. Both of the explanatory variables are related to the response variable. C. Exactly one of the explanatory variables is related to the response variable. D. At least one of the explanatory variables is significantly related to the response variable.

D. At least one of the explanatory variables is significantly related to the response variable.

Refer to the portion of regression results in the accompanying table. df SS MS F Significance F Regression 2 3,500. 1,750 0.1000 Residual 20 13,500. 675 Total. 22. 17,000 When testing the overall significance of the regression model at the 5% level given a critical value of F0.05,(2,20) = 3.49, the decision is to A. reject H0 and conclude that the explanatory variables are jointly significant B. not reject H0 and conclude that the explanatory variables are jointly significant C. reject H0 and conclude that the explanatory variables are not jointly significant D. not reject H0 and conclude that the explanatory variables are not jointly significant

D. not reject H0 and conclude that the explanatory variables are not jointly significant

ANOVA is a statistical technique used to determine if differences exist between the means of two populations.

FALSE

Simple linear regression includes more than one explanatory variable.

FALSE

The correlation coefficient can only range between 0 and 1.

FALSE (-1 </= RXY </= 1)

A simple linear regression model uses one explanatory variable to explain the variability in the response variable.

TRUE

ANOVA is a statistical technique used to determine if differences exist between the means of three or more populations.

TRUE

When using Fisher's least difference (LSD) method at some stated significance level α, the probability of committing a Type I error increases as the number of pairwise comparisons increases.

TRUE