Use the data below to answer the parts of the questions using regression analysi
ID: 3325059 • Letter: U
Question
Use the data below to answer the parts of the questions using regression analysis. Use Academic Reputation as the dependent variable. Include all of the other five variables as independent variables.
A) What hypothesis test on the regression output allows you to test if this model has any statistically significant explanatory power? Does this model have any statistically significant explanatory power at the 1% level?
B) Which variables are significant at the 10% level?
C) Use this model to estimate the Academic Reputation of a university with the following characteristics: Financial Aid=8, Cost=30, Early Pay=60, Better Place=70, and STEM=40.
D) Which university has a residual with the largest absolute value? What is the standardized residual for this university? For this university, which predictor of the five variables has the largest absolute value z-score?
Excel Info:
University Academic Rep. Score Financial Aid Cost Early Pay Better Place (%) STEM (%) 1 98 10.40 28.83 61.40 66 28 2 92 8.64 41.38 74.90 57 79 3 92 9.63 38.61 65.90 62 29 4 97 9.47 42.66 60.20 58 29 5 96 9.94 36.85 60.30 69 21 6 90 7.86 45.47 72.60 65 93 7 90 9.52 40.81 56.30 45 20 8 92 8.87 43.57 60.30 53 19 9 92 8.28 48.47 60.60 58 35 10 88 8.61 45.80 57.50 64 26 11 85 9.72 39.52 57.30 56 25 12 84 8.33 47.45 59.70 54 33 13 100 8.92 80.46 61.30 59 32 14 87 8.24 46.16 57.10 55 22 15 83 7.59 39.83 63.90 62 43 16 83 7.57 49.89 57.40 50 22 17 89 7.48 57.61 56.30 55 23 18 80 8.03 52.14 51.80 49 7 19 96 6.99 63.98 50.60 56 22 20 79 4.04 32.22 59.50 51 31 21 81 7.40 52.94 51.30 57 14 22 87 6.53 65.62 55.50 52 25 23 76 4.23 25.48 54.70 53 24 24 69 2.97 18.15 62.50 43 71 25 74 7.57 55.14 53.00 50 13 26 77 4.20 29.63 51.80 47 21 27 76 6.09 66.54 64.70 48 51 28 70 7.93 49.94 53.10 43 10 29 74 3.31 29.03 58.00 49 28 30 65 7.16 50.84 60.40 43 37 31 73 7.29 55.05 54.20 62 23 32 67 8.37 46.11 45.30 43 16 33 65 6.53 55.79 58.40 49 52 34 73 3.15 21.99 46.20 47 15 35 67 3.97 27.01 52.40 59 38 36 76 5.83 65.80 49.10 45 12 37 65 4.58 26.19 49.40 49 16 38 67 4.08 29.62 5.10 59 34 39 63 3.53 18.88 53.50 58 25 40 68 3.60 26.37 45.90 55 15 41 61 4.03 25.83 49.90 52 30 42 71 6.48 61.91 51.40 46 33 43 51 6.38 63.21 66.80 47 84 44 63 5.38 71.25 63.30 46 74 45 64 2.85 33.16 56.40 51 26 46 47 6.86 38.72 59.40 50 69 47 59 7.50 50.73 48.30 49 4 48 57 2.45 26.01 55.50 53 31 49 64 6.62 57.46 49.30 45 20 50 64 5.57 63.58 55.00 51 23Explanation / Answer
The regression summary output with excel is Given below
A) What hypothesis test on the regression output allows you to test if this model has any statistically significant explanatory power? Does this model have any statistically significant explanatory power at the 1% level?
Here ANOVA test on the regression allows to test if the model has any statisticallty significant power. Here this is evaluated by F value which is 12.1885 which is significant in nature as p - value is less than 0.01 so we can say that model is significant in nature.
(B) Which variables are significant at the 10% level?
Except Cost, all other four variables are significant at 10 % level as p - value associated with each of the variable is less than 0.10.
(C) Use this model to estimate the Academic Reputation of a university with the following characteristics: Financial Aid=8, Cost=30, Early Pay=60, Better Place=70, and STEM=40.
Answer :
Academic Reputation = 5.6294 + 2.3787 * Financial aid + 0.0183 * cost + 0.3181 * Early Pay + 0.7944* Better Place (%) - 0.1709 * (STEM %)
= 5.6294 + 2.3787 * 8+ 0.0183 * 30 + 0.3181 * 60 + 0.7944 * 70 - 0.1709 * 40 = 93.066
(c) Which university has a residual with the largest absolute value? What is the standardized residual for this university? For this university, which predictor of the five variables has the largest absolute value z-score?
Here the EXCEL summary for residuals are given below.
So here we can see in column 3 that the maximum residual is for University 46
Standardised residual for this university is -2.64106
For this predictor, the largest z score is for STEM % as mean STEM % is 31.46% and the university 46 has 69%.
SUMMARY OUTPUT Regression Statistics Multiple R 0.762052 R Square 0.580723 Adjusted R Square 0.533078 Standard Error 8.983086 Observations 50 ANOVA df SS MS F Significance F Regression 5 4917.804 983.5607 12.1885 1.94E-07 Residual 44 3550.616 80.69583 Total 49 8468.42 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 5.629441 13.97394 0.402853 0.689007 -22.5332 33.79207 -22.5332 33.79207 Financial Aid 2.378709 0.805036 2.954787 0.00501 0.756266 4.001152 0.756266 4.001152 Cost 0.018344 0.102986 0.178124 0.859443 -0.18921 0.225899 -0.18921 0.225899 Early Pay 0.318137 0.168186 1.891582 0.06514 -0.02082 0.657092 -0.02082 0.657092 Better Place (%) 0.794428 0.226332 3.510012 0.001047 0.338286 1.250571 0.338286 1.250571 STEM (%) -0.17094 0.076874 -2.22358 0.031358 -0.32587 -0.01601 -0.32587 -0.01601Related Questions
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