Question

The answers are marked but I need them explained.

A new program designed to improve high school student reading comprehension has been launched in a major school district. Students can choose how many hours they spend participating in the program, as an alternative to some other elective courses. A researcher is interested in a possible linear relationship between the number of hours a student spends taking part in the program (X) and standardized reading test scores (Y). 100 students were sampled in the study b 64.51 b 23.47 se(b)-9.2 SST 10432 MSE 100.44 13. What is the interpretation of the y-intercept from the regression results above? A 1-hour increase in program participation is associated with an increase in predicted reading scores of 64.51 A 1-hour increase in program participation is associated with a decrease in predicted reading scores of 23.47 The predicted reading score of a student who spends 0 hours participating in the program is 64.51. The maximum reading score on the test is 64.51 The minimum reading score on the test is 64.51 a. b. d. e. 14. What is the interpretation of the regression coefficient from the results above'? A 1-hour increase in program participation is associated with a decrease in predicted reading scores of 23.47 The predicted reading score of a student who spends 0 hours participating in the program is 64.51 A 1-hour increase in program participation is associated with an increase in predicted a. b. c, read ing scores of 64.51 d. A 1-hour increase in program participation is associated with an increase in predicted reading scores of 23.47. e. The maximum reading score on the test is 64.51 15. What is the calculated value (test statistic) for a test on the overall model? a. 9.03 b. 5.86 c. 3.36 e. 6.27 16. What is the calculated value (test statistic) for a test on bi? a. 2.55 b. 1.39 c. 6.02 d. 7.41 e. 11.89 17. What is the null hypothesis for the test in #16? e. 18. What is the value of R2? a. 4659 b. .0598 c. .9435 d. 0565 e. This value cannot be determined based on the information provided. 19. What is the predicted reading score of a student who spends 3.5 hours in the new program? a. 64.51 b. 146.7 c. 199.4 d. 88.67 e. 23.47 20. What is the critical value for the test on the overall model? a. 4.00 b. 8.21 c. 2.02 d. 6.45 e. 1.00 21. Based on the result of the test on the overall model, which of the following is true regarding the p-value associated with this test? a. The p-value is greater than 64.51 b. The p-value is greater than 9.2. The p-value is less than.05. The p-value is greater than 4 Nothing can be said about the elusive p-value. d. e.

Answer 1

Ans:

13,14)Regression equation:

y'=64.51+23.47x

slope coefficient=23.47

y-intercept=64.51

(i.e. when x=0,y'=64.51)

slope coefficient indicates the average increase or decrease in y per unit increase or decrease in x.

15)

source	DF	SS	MS	F
regression	1	588.88	588.88	5.86
error	98	9843.12	100.44
Total	99	10432

SS(error)=98*100.44=9843.12

SS(regression)=10432-9843.12=588.88

MS=SS/df

F=588.88/100.44=5.86

16)

Test statistic:

t=b₁/se(b₁)

t=23.47/9.2

t=2.55

17)

$H_0:\beta_1=0$

$H_a:\beta_1\neq 0$

18)

R^2=SSR/SST=588.88/10432=0.0565

19)

y'=64.51+23.47*3.5=146.7

20)critical F value=FINV(0.05,1,98)=4.00

21)n=100

df=n-2=100-2=98

p-value=tdist(2.55,98,2)=0.0123

p-value is less than 0.05