4 pts Many colleges and universities develop regression models for predicting the GPA of incoming freshmen. This predicted GPA can then be used to make admission decisions. Although most models use many independent variables to predict GPA, in this case the following two variables were selected: . Verbal score on college entrance examination (percentile) . Mathematics score on college entrance examination (percentile) Based on a random sample of 40 freshmen at one college, a first order multiple regression model using these two independent variables was fitted to predict GPAs. Using RStudio, the following scatter plots and regression output were generated: Files Plots Packages Help Viewer Presentation 1 zoom Export . Publish .18 3.5 A 3.0 GPA GPA O arch NFiles Plots Packages Help Viewer Presentation zoom Export - Publish . 160 OO O O O 3.0 O GPA GPA O O 40 50 60 70 80 90 50 60 70 80 90 100 VerbalScores MathScores Console Terminal * Background Jobs * R R4.2.1 . ~/ > model summary (model) Search W NGPAs to fall within plus or minus .8046 units of the predicted GPAs. Question 6 3 pts Based on the regression output shown above in Question 4, which independent variable(s) has/have a statistically significant linear relationship with GPA at the alpha = 0.01 level? O Only the independent variable Verbal Score has statistically significant linear relationship with GPA O None of the independent variables have statistically significant linear relationship with GPA O Only the independent variable Math Score has statistically significant linear relationship with GPA O Both of the independent variables have statistically significant linear relationship with GPA Question 7 3 pts Q Search W N40 50 60 70 80 90 50 60 70 80 90 100 VerbalScores MathScores Console Terminal x Background Jobs x R R4.2.1 . -/ > model|t|) (Intercept) -1. 570537 0. 493749 -3. 181 0. 00297 verbalscores 0. 025732 0. 004024 6. 395 1. 83e-07 * *# Mathscores 0. 033615 0. 004928 6. 822 4. 90e-08 * * * Signif. codes : 0. 001 .* *' 0. 01 =' 0. 05 '. ' 0.1 .' 1 Residual standard error: 0. 4023 on 37 degrees of freedom Multiple R-squared: 0. 6811, Adjusted R-squared: 0. 6638 F-statistic: 39. 51 on 2 and 37 DF, p-value: 6. 585e-10 > Based on the regression output shown above, which of the following statement is corre the overall usefulness of this model at the alpha = 0.01 level? This model is overall useful because we have strong enough statistical evidence to conclude th of the two slopes estimated is not zero. This can be seen from the F test statistic of 39.51 and corresponding p-value = 6.585e-10 which is less than alpha of 0.01 This mortal is overall not nicoful hacauce the ortimate for the clone acenciator with Vorhal Cron archSignif. codes : 0 ' 0. 001 ' WW' 0. 01 . "' 0. 05 .. 0. 1 . ' 1 Residual standard error: 0. 4023 on 37 degrees of freedom Multiple R-Squared: 0. 6811, Adjusted R-squared: 0. 6638 F-statistic: 39. 51 on 2 and 37 DF, p-value: 6. 585e-10 Based on the regression output shown above, which of the following statement is correct regarding the overall usefulness of this model at the alpha = 0.01 level? O This model is overall useful because we have strong enough statistical evidence to conclude that at least one of the two slopes estimated is not zero. This can be seen from the F test statistic of 39.51 and the corresponding p-value = 6.585e-10 which is less than alpha of 0.01 This model is overall not useful because the estimate for the slope associates with Verbal Score (our first chosen predictor) is statistically not different from zero. This can be seen from the t-value = 6.395 and the corresponding p-value = 1.83e-07 which is less than alpha of 0.01 This model is overall useful because the R-squared Adjusted value of 0.6638 is relatively large and it is bigger than alpha of 0.01 O This model is overall useful because the slope associates with Math Scores (our second chosen predictor) is shown to be statistically different from zero. This can be seen from t-value , 6.822 and the corresponding p- value = 4.90e-08 which is less than alpha of 0.01 Question 5 3 pts Search W N