ACT GPA 21 3.897 14 3.885 28 3.778 22 2.54 21 3.028 31 3.865 32 2.962 27 3.961 2
ID: 3056626 • Letter: A
Question
ACT GPA
21 3.897
14 3.885
28 3.778
22 2.54
21 3.028
31 3.865
32 2.962
27 3.961
29 0.5
26 3.178
24 3.31
30 3.538
24 3.083
24 3.013
33 3.245
27 2.963
25 3.522
31 3.013
25 2.947
20 2.118
24 2.563
21 3.357
28 3.731
27 3.925
28 3.556
26 3.101
28 2.42
22 2.579
26 3.871
21 3.06
25 3.927
16 2.375
28 2.929
26 3.375
22 2.857
24 3.072
21 3.381
30 3.29
27 3.549
26 3.646
26 2.978
30 2.654
24 2.54
26 2.25
29 2.069
24 2.617
31 2.183
15 2
19 2.952
18 3.806
27 2.871
16 3.352
27 3.305
26 2.952
24 3.547
30 3.691
21 3.16
20 2.194
30 3.323
29 3.936
25 2.922
23 2.716
25 3.37
23 3.606
30 2.642
21 2.452
24 2.655
32 3.714
18 1.806
23 3.516
20 3.039
23 2.966
18 2.482
18 2.7
29 3.92
20 2.834
23 3.222
26 3.084
28 4
34 3.511
20 3.323
20 3.072
26 2.079
32 3.875
25 3.208
27 2.92
27 3.345
29 3.956
19 3.808
21 2.506
24 3.886
27 2.183
25 3.429
18 3.024
29 3.75
24 3.833
27 3.113
21 2.875
19 2.747
18 2.311
25 1.841
18 1.583
20 2.879
32 3.591
24 2.914
35 3.716
25 2.8
28 3.621
28 3.792
25 2.867
22 3.419
30 3.6
20 2.394
20 2.286
31 1.486
20 3.885
29 3.8
28 3.914
16 1.86
28 2.948
at a small college selected 120 students at random from the new freshman class in a study to determine whether a student's grade point average (GPA) at the end of the freshman year can be predicted from their ACT test score. The data can be found at 1. The director of admissions "GPA.txt" a. Fit a simple linear regression using ACT score as the explanatory variable, and GPA as the response variable. Verify all necessary model assumptions and include all necessary plots; b. Estimate the parameter ; c· Use a t-test to determine whether or not there a linear relationship between ACT score and GPA: d. Compute the ANOVA table corresponding to the model; From the table determine the mean square error (MSE) f· Use the ANOVA F-test to determine whether or not there is a linear relationship between ACT score and GPA; g. How do the results in (e) compare to those in (b)? h. How do the results in (f) compare to those in (c)? i. What proportion of the variation in GPA is explained by the re- gression model?Explanation / Answer
We use Minitab to solve this question.
Regression Analysis: GPA versus ACT
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 3.588 3.5878 9.24 0.003
ACT 1 3.588 3.5878 9.24 0.003
Error 118 45.818 0.3883
Lack-of-Fit 19 6.486 0.3414 0.86 0.632
Pure Error 99 39.332 0.3973
Total 119 49.405
Model Summary
S R-sq R-sq(adj) R-sq(pred)
0.623125 7.26% 6.48% 3.63%
Coefficients
Term Coef SE Coef T-Value P-Value VIF
Constant 2.114 0.321 6.59 0.000
ACT 0.0388 0.0128 3.04 0.003 1.00
Regression Equation
GPA = 2.114 + 0.0388 * ACT
___________________________________________________________________________________________
b) Estimated parmeter of sigma is 0.623125.
c) The t value is 3.04 & p- value is 0.003 therefore their is correlation between ACT score and GPA
d)
Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 3.588 3.5878 9.24 0.003
ACT 1 3.588 3.5878 9.24 0.003
Error 118 45.818 0.3883
Lack-of-Fit 19 6.486 0.3414 0.86 0.632
Pure Error 99 39.332 0.3973
Total 119 49.405
MSE = 0.3883
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