Use the following information to answer questions 18-21. The data below are the

ID: 3375988 • Letter: U

Question

Use the following information to answer questions 18-21. The data below are the number of absences and the final grades of 9 randomly chosen students from a statistics class Number of absences,x 0 3 64 9215 8 5 988680 8271 92 55 76 82 Final grade, y x- 52, y 722, x2-460, y-59154, xy 3732 18. Find the sample correlation coefficient r. (a) .5000 (b) -.6255 (c) .6255 (d) .9908 (e) -.9908 19. We would like to test whether there is significant linear relationship between number of absences and Final Grade, i.e., Ho : -0 versus Ha : -0. The value of the test statistic for this test is closestto (a) -19.37 (b)19.37 (c) -.9908 (d) 2.5719 (e) 0 20. Find the rejection region at a.02 significance level and state your conclusion (a) Rejection region: t2.998; Decision: Reject Ho (b) Rejection region: t

Explanation / Answer

Solution

The linear regression model is: Y = ?0 + ?1X + ?

NOTE

Answer to the point are given below. Details follow at the end.

Part (a)

Sample correlation coefficient, r = 0.99078 Option (d) ANSWER

Part (b)

Test statistic, t = - 19.3515 Option (b) ANSWER

Part (c)

Rejection region: | t | > 2.998 and Decision: Reject H0. Option (a) ANSWER

Part (d)

Predicted Final Grade of Student A = 76.855. No prediction is permissible for Student B because the absentee days of 25 goes beyond the given range of x and extrapolation is not permitted in regression prediction. Option (c) ANSWER

Details

Given

n =

?x =

?y =

722

?x^2 =

460

?y^2 =

59154

?xy =

3732

? =

0.02

Calculations

Xbar =

(?x)/n

5.777778

Ybar =

(?y)/n

80.22222

Sxx =

(?x^2) - nXbar^2

159.5556

Syy =

(?y^2) - nYbar^2

1233.556

Sxy =

(?xy) - n(Xbar)(Ybar)

-439.556

?1cap =

Sxy/Sxx

-2.75487

?0cap =

Ybar - (?1cap)Xbar

96.13928

r =

Sxy/?(Sxx.Syy)

-0.99078

r^2 =

0.981651

Test Statistic, t, for

? = 0

r ?{(n - 2)/(1 - r^2)}

-19.3515

tcrit =

t(n - 2, ?/2)

2.997952

x0 =

ycap at x0

76.85515