You are testing the null hypothesis that there is no relationship between two variables, X and Y

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You are testing the null hypothesis that there is no relationship between two variables, X and Y. From your sample of n = 22, you determine that SSR = 60 and SSE=20. Complete parts (a) through (e) below. a. What is the value of FSTAT? State the hypotheses to test. Choose the correct answer below. O A. Ho B, 70 Hi: B, = 0 0C. Ho: B, 50 H: 8,0 O B. Ho B.20 HB,0 D. Ho B.= 0 H: B, 0 FSTAT = 60.0 (Round to the nearest integer as needed.) b. At the a= 0.05 level of significance, what is the critical value? The critical value is 4.35 (Round to two decimal places as needed.) c. Based on your answers to (a) and (b), what statistical decision should you make? A. Reject Ho. There is evidence that there is a relationship between X and Y. OB. Do not reject Ho. There is evidence that there is a relationship between X and Y. OC. Do not reject Ho. There is no evidence that there is a relationship between X and Y. OD. Reject Ho. There is no evidence that there is a relationship between X and Y. d. Compute the correlation coefficient by first computing r and assuming that b, is negative. 2= (Round to four decimal places as needed.)



Solution :

a) Null and alternative hypotheses :

Ho: B1 = 0

H: B170

Test statistic :

The value of the F-test statistic is given as follows :

FST AT MSR MSE

Where, MSR is the mean square due to regression and MSE is the mean square due to error.

SSR MSR= SSE and MSE DF Reg DF Error

DFReg = p - 1

DFError = n - p

(k is the number of parameters and n is the sample size.)

We have, SSR = 60, SSE = 20, n = 22, p = 2

DFReg = (2 - 1) = 1

DFError = (22 - 2) = 20

60 MSR= = 60 20 and MSE = 20

60 .. FST AT - 60

b) Critical value :

Significance level = 0.05

DF = (1, 20)

Using F-table we get,

Critical value = 4.35

c) Decision :

Since value of the test statistic is greater than the critical value therefore we shall reject Ho at 0.05 significance level.

Conclusion :

Reject Ho. There is evidence that there is a relationship between X and Y.

d) The r2 is given as follows :

p2 SSR TSS

Where, sum of square due to regression and TSS is the total sum of squares.

TSS = SSR + SSE

TSS = 60 + 20

TSS = 80

08 al 09

2 = 0.7500

ir= V0.7500

..r=0.8660

The correlation coefficient is 0.8660.