Question

Given are five observations for two variables, r and y. 3 4 5 1 2 7 6 11 14 4 The estimated regression equation is y = 1.2 + 2.4r Compute the mean square error using the following equation (to 3 decimals). a. SSE s2=MSE n- 2 decimals). b. Compute the standard error of the estimate using the following equation (to SSE VMSE Vn-2 SE c. Compute the estimated standard deviation bi using the following equation (to 3 decimals). Sp VΣ(,-3 m d. Use the t test to test the following hypotheses (a= 05 ): Ho: B 0 H, B0 Compute the value of the t test statistic (to 2 decimals). The p-value is - Select your answer Use Table 1 of Appendix B. What is your conclusion? -Select your answer e. Use the F test to test the hypotheses in part (d) at a .05 level of significance. Complete the F table below. Calculate the Sum of Squares (to 1 decimal), the Mean Squares (to 3 decimals), F ratio (to 2 decimals) and the p-value (to 4 decimals). F Mean Square Sum of Squares p-value Source of Variation Degrees of Freedom Regression Error Total What is the p-value? - Select your answer-

Answer 1

(x-x)2 (v-y} (x-x(y- X S.No 4. 1 1 4.0000 19.3600 8.8000 7 1.0000 2 2 1,9600 1.4000 6 0.0000 5.7600 0.0000 4 4 11 1.0000 6.7600 2.6000 5 5 14 4.0000 31.3600 11.2000 Total 15 42 10.0000 65.2000 24.0000 3.0000 8.4000 Mean SSX SSY SXY SST-Syy= 65.2000 SSE =Syy-(Sxy)/Sxx = Sxy)/Sxx 7.6000 SSR 57.6000 s2-SSE/(n-2) se -s error Variance o 2.533 std error o 1.5916 null hypothesis: 0 Alternate Hypothesis: 0 for 0.05 level,two tailed test and n-2= 3 degree of freedom, critical t 3.1824 reject Ho if absolute value of test statistic t>3.182 Decision rule s/NSm estimated standard error of slope =se(B) 0.5033 B/se(B,) test stat t 4,7683 st LO

from above:

a)

s² =2.533

b)

s =1.592

c)

sb1 =0.503

d)

test statistic t =4.77

the p value 0.0175

e)

Source	DF	SS	MS	F	p value
regression	1	57.6	57.600	22.74	0.0175
Residual error	3	7.6	2.533
Total	4	65.2