Question

A study was conducted to determine whether a the final grade of a student in an introductory psychology course is linearly related to his or her performance on the verbal ability test administered before college entrance. The verbal scores and final grades for 1010 students are shown in the table below.

Student	Verbal Score x	Final Grade y
1	62	72
2	60	76
3	76	93
4	60	69
5	77	88
6	27	31
7	80	96
8	76	89
9	62	71
10	76	92

Compute the value of SST (Total Sum of Squares)
answer:

Compute the value of SSR (Regression Sum of Squares)
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Compute the value of SSE (Error Sum of Squares)
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The coefficient of determination is
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What percent of variation in the observed values of the response variable is explained by the regression?
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Answer 1

Using Minitab software, (Stat -> Regression -> Regression), we get the following output :

Now,

The value of SST (Total Sum of Squares) = 3344.1

The value of SSR (Regression Sum of Squares) = 3282.39

The  value of SSE (Error Sum of Squares) = 61.71

The coefficient of determination is =R² = 98.15%

98.15% of variation in the observed values of the response variable is explained by the regression