Linear Regression Analysis: Predicting Sociology Grades based on Verbal Ability Scores, Exercises of Statistics

An example of linear regression analysis using minitab statistical software. The data consists of verbal ability test scores (x) and final sociology grades (y) for ten students. The regression equation is derived, and the correlation coefficient, standard deviation, and analysis of variance are provided. The document also includes predictions of individual values of y and the mean of y for a given value of x, along with their respective confidence intervals.

Typology: Exercises

2019/2020

Uploaded on 06/15/2020

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MTB > # problem 11.77 STA 3123
MTB > # example of linear regression and correlation
MTB >
MTB > set c1
DATA> 39 43 21 64 57 47 28 75 34 52
DATA> end
MTB > set c2
DATA> 65 78 52 82 92 89 73 98 56 75
DATA> end
MTB > name c1 'x' c2 'y'
MTB > # x is verbal ability test score
MTB > # y is final sociology grade
MTB >
MTB > print 'x' 'y'
ROW x y
1 39 65
2 43 78
3 21 52
4 64 82
5 57 92
6 47 89
7 28 73
8 75 98
9 34 56
10 52 75
MTB > gstd
* NOTE * Standard Graphics are enabled.
Professional Graphics are disabled.
Use the GPRO command to enable Professional Graphics.
MTB > plot 'y' vs 'x'
y - *
-
- *
90+ *
-
-
- *
- *
75+ *
- *
-
- *
-
60+
- *
pf3

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MTB > # problem 11.77 STA 3123 MTB > # example of linear regression and correlation MTB > MTB > set c DATA> 39 43 21 64 57 47 28 75 34 52 DATA> end MTB > set c DATA> 65 78 52 82 92 89 73 98 56 75 DATA> end MTB > name c1 'x' c2 'y' MTB > # x is verbal ability test score MTB > # y is final sociology grade MTB > MTB > print 'x' 'y'

ROW x y

1 39 65 2 43 78 3 21 52 4 64 82 5 57 92 6 47 89 7 28 73 8 75 98 9 34 56 10 52 75

MTB > gstd

  • NOTE * Standard Graphics are enabled. Professional Graphics are disabled. Use the GPRO command to enable Professional Graphics.

MTB > plot 'y' vs 'x'

y - *

90+ *

75+ *

60+

+---------+---------+---------+---------+---------+------x 20 30 40 50 60 70

MTB > regress 'y' on 1 predictor variable 'x'

The regression equation is y = 40.8 + 0.766 x

Predictor Coef Stdev t-ratio p Constant 40.784 8.507 4.79 0. x 0.7656 0.1750 4.38 0.

s = 8.704 R-sq = 70.5% R-sq(adj) = 66.8%

Analysis of Variance

SOURCE DF SS MS F p Regression 1 1450.0 1450.0 19.14 0. Error 8 606.0 75. Total 9 2056.

MTB > # to predict individual value of y and MTB > # mean of y for a given value of x MTB > MTB > regress 'y' on 1 'x'; SUBC> predict y for x equal to 50; SUBC> predict mean y for x equal to 35.

The regression equation is y = 40.8 + 0.766 x

Predictor Coef Stdev t-ratio p Constant 40.784 8.507 4.79 0. x 0.7656 0.1750 4.38 0.

s = 8.704 R-sq = 70.5% R-sq(adj) = 66.8%

Analysis of Variance

SOURCE DF SS MS F p Regression 1 1450.0 1450.0 19.14 0. Error 8 606.0 75. Total 9 2056.

Fit Stdev.Fit 95% C.I. 95% P.I. 79.06 2.84 ( 72.51, 85.61) ( 57.94, 100.18)