please show all the work with explanations. thanks linear regression equation ý

Question

please show all the work with explanations. thanks

linear regression equation ý 29.79-0.73x. Suppose also that SSE 6.271, SSR-37.157, and (x-X)2-70 22. Suppose that a sample data set containing 7 observations results in the estimated a. Conduct a t-test at the 0.05 significance level to determine if there is a statistically significant linear relationship between x and y based on this sample. Hb0yueul for pare di cn y Test Statistic (Show all work here): 0 -1.30-210 , 1.12 Rejection decision (Explain): p0 ect nult vut Conclusion (Interpret the rejection decision): e failed enagn evidence b. Conduct an F-test at the 0.05 significance level to determine if there is a statistically significant linear relationship between x and y based on this sample. Ho : Ha = Test Statistic (Show all work here): Rejection decision (Explain): Conclusion (Interpret the rejection decision):

Explanation / Answer

22. b)

H0: There is no statistically significnat linear relationship between x and Y
H1: There is statistically significnat linear relationship between x and Y
Let the los be alpha = 5% = 0.05

Mean SSE = SSE / n-2 = 6.271/(7-2) = 1.2542
Mean SSR = SSR / 1 = 37.157/1 = 37.157

Test Statistic F = Mean SSE . Mean SSR = 37.157/1.2542 = 29.6261

Reject H0: if F value > F crtical value (=6.608),

Conclustion: Here F value 29.6261 > F critical value so we reject H0

Thus we conclude that There is statistically significnat linear relationship between X and Y

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