Question

A study was conducted to detemine 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 xx	Final Grade yy
11	3535	4141
22	8080	9292
33	5656	6363
44	3434	3636
55	6464	7474
66	3333	3535
77	5757	7070
88	3131	3636
99	2727	3131
1010	7070	8484

Find the least squares line.

y^=y^=  ++  xx

Should the regression be used to predict the final grade of a student with a verbal score of 100?
answer:

Answer 1

The least square regression equation is ,

                                  y = a + b * x

      where , y^ = dependent variable = Final Grade

                    x = independent variable= Verbal Score

                    a = intercept

                    b = slope

In excel we can calculate a and b by using the following commands,

For intercept(a)                                = INTERCEPT(KNOWNY_Y,KNOWN_X)

For slope ( b )                                    = SLOPE(KNOWNY_Y,KNOWN_X)

We get a = -2.583 and b = 1.207

We get the least square regression equation as

                                              

when Verbal score= x = 100 then calculate predicted final score= y^ = ?

By using the least square regression equation,

  

Therefore predicted final score=