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2. The mathematics department at a university is interested in learning more about the grades that students carn in an introductory calculus class. A sample of n = 80 students who have taken this introductory calculus course during any semester of the three last three academic years is selected. The academic record for each selected student is reviewed. The professors in the math department determine that, of the available information for all students, the relevant variables are their final grade in the calculus course, their high school percentile rank, their score on the algebra placement test given to all incoming students who plan to take a calculus course, their ACT Math score, and their ACT Natural Sciences score. A. The professors in the math department believe that the score on the algebra placement test and the high school percentile rank will be the best explanatory variables for the final grade in calculus. The partially complete ANOVA table below shows relevant values for the model containing these two explanatory variables. Conduct the F test for whether this model is useful or not. SS df MS F p-value Regression 2810.4 2 1420.2 Residuals 7491.8 77 97.3 Total 10332.2 79 B. What is the minimum number of values that need to be known to be able to fill in the ANOVA table completely? C. One of the professors suggests testing whether adding the two ACT scores to the regression model would improve the model. The ANOVA table below shows the relevant values for the model containing all four explanatory variables. Conduct the appropriate F test to determine if adding the ACT scores improves the model. SS df MS F p-value Regression 2986.2 1 746.5 7.6 3.50-5 Residuals 7316.0 75 97.9 Total 10332.2 79 D. Which of the two suggested models should the math department use? E. In an attempt to further improve the model, the professors decide to look at the a t-tests for each of the coefficients in the model that you chose in part D.. Using the Python output for both models shown below, conduct each t-test for slope. coef std err P>It| [0. 025 0.975] const 43 . 8685 8.375 5.238 0.090 27 . 193 60.544 HSRank 0. 1812 0. 096 1.896 0. 062 -0.009 0. 372 Algebra 1. 0499 0. 247 4.248 0.090 0.558 1.542coet std err t P> t [0. 025 0.975] const 36. 1215 10.752 3.360 0.001 14.703 57.540 HSRank 0. 1353 0. 104 1. 306 0. 196 -0. 071 0. 342 Algebra 0. 9610 0. 264 3. 640 0.000 0.435 1.487 ACTM 0. 2718 0. 454 0. 599 0.551 -0.632 1. 175 ACTNS 0. 2161 0. 313 0. 690 0. 492 -0. 408 0. 840 F. Based on the conclusions from part E., which explanatory variable, if any, would you try removing first
