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The data shown below for the dependent variable, y, and the independent variable, x, have been collected using simple random sampling. X 10 15 11 19 18 17 5 17 18 y 9070 30 8020 30 5060 40 40 a. Develop a simple linear regression equation for these data. b. Calculate the sum of squared residuals, the total sum of squares, and the coefficient of determination c. Calculate the standard error of the estimate. d. Calculate the standard error for the regression slope. e. Conduct the hypothesis test to determine whether the regression slope coefficient is equal to O. Test using α =0.05. Click the icon to view the t-distribution table a. Complete the linear regression equation below. Round to one decimal place as needed.)b. Calculate the sum of the squared residuals. SSE-1 (Round to the nearest whole number as needed.) What is the total sum of squares? SST(Round to the nearest whole number as needed.) Determine the coefficient of determination. R2(Round to two decimal places as needed.) c. What is the standard error of the estimate? (Round to two decimal places as needed.) d. Determine the standard error for the regression slope. sb(Round to two decimal places as needed.)Determine the rejection region for the test statistic t. Select the correct choice below and fill in any answer boxes to complete your choice. Round to four decimal places as needed.) Calculate the simple linear regression test statistic t. □ (Round to four decimal places as needed.) Since the test statisticin the rejection region, ! the null hypothesis. Conclude that the regression model ▼| significant. This means that knowing x | ▼| useful help in predicting

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(х-х) 32.4900 0.4900 1.6900 22.0900 10.8900 5.2900 1.6900 0.4900 1.6900 5.2900 82.1000 S.No (y-y) 10 1521.0000 361.0000 441.0000 841.0000 961.0000 441.0000 1.0000 81.0000 121.0000 121.0000 4890.0000 222.3000 13.3000 27.3000 -136.3000 102.3000 -48.3000 1.3000 -6.3000 14.3000 25.3000 597.0000 70 30 19 18 17 15 17 18 157 15.7000 30 10 Total 510 Mean 51.0000 SSX sample size: here 51.0000 15.7000 from above 82.1000 6.086 597.0000 slope- 7.27162 intercept- 165.16443 hence line equation: 165.1644 7.2716 x total sum of square SST 4890.0000 regression sum of square SSR- 4341.157 Error sum of square SSE- 548.843 SSE error variance ơ2_ s2 -SSE/(n-2) 68.6054 std error σ null hypothesis: Alternate Hypothesis: for 0.05 level,two tailed test and n-2-8 degree of freedom, critical t- Decision rule: 2.3060 reject Ho if absolute value of test statistic t>2.306 estimated standard error of slope se(B) 0.9141 test stat t- A/se(61)- 7.9547

a)

yhat=165.2+(-7.3)x

b)

SSE =548.843~ 549

SST =4890

R2 =0.89

c)

se =8.28

d)

sb1=0.91

rejection region: option A: t<-2.3060 or t>2.3060

t =-7.9547

since the test statsitic is in rejetion reigon ; reject...model is significant...knowing x is useful

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