Question

A study was conducted to determine whether 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 10 students are shown in the table below.

Student	Verbal Score xx	Final Grade yy
1	35	91
2	64	74
3	46	61
4	35	98
5	79	95
6	53	88
7	63	83
8	54	98
9	37	99
10	42	72

Find the following:

The least squares line: ŷ =

Calculate the residual for the second student:

Answer 1

The following data are passed:

X	Y
35	91
64	74
46	61
35	98
79	95
53	88
63	83
54	98
37	99
42	72

The independent variable is X, and the dependent variable is Y. In order to compute the regression coefficients, the following table needs to be used:

	X	Y	X*Y	X2	Y2
	35	91	3185	1225	8281
	64	74	4736	4096	5476
	46	61	2806	2116	3721
	35	98	3430	1225	9604
	79	95	7505	6241	9025
	53	88	4664	2809	7744
	63	83	5229	3969	6889
	54	98	5292	2916	9604
	37	99	3663	1369	9801
	42	72	3024	1764	5184
Sum =	508	859	43534	27730	75329

Based on the above table, the following is calculated:

Therefore, based on the above calculations, the regression coefficients (the slope m, and the y-intercept n) are obtained as follows:

Therefore, we find that the regression equation is:

Second Student

When X = 64

Residual for the second student is:

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