Question

Section 12.3 Multiple Linear Regression:

Number ONE:

Statistical software was used to fit the model E(y)Pox1 2x2 to n 20 data points. Complete parts a through h EEB Click the icon to see the software output. Data Table The regression equation is Y-1738.93 - 384.54x1 517.39x2 Predictor Constant X1 X2 Coef 1738.93 - 384.54 -517.39 SE Coef 369.06 101.65 - 3.78 0.002 353.04 - 1.47 0.162 4.71 0.000 s-172.003 R-sq-55.0% R-sq(adj):49.0% Analysis of Variance MS Source Regression Residual Error 17 Total DF 2 609,768 304,884 10.31 0.001 29.585 502,948 19 1,112,716 a. What are the sample estimates of βο-β1 , and β2? Type integers or decimals.) b. What is the least squares prediction equation? Type integers or decimals.) c. Find SSE, MSE, and s. Interpret the standard deviation in the context of the problem. SSE MSE xory? Type an integer or a decimal) Interpret the value of s The interval ±2s w within about +2s provide a rough approximation to the accuracy with which he model ill predict future values of or i en a ues o Thus t would be expected hat emo e ill provide red so to d. Test Ho: β,-0 against Ha: β1 #0. Use α: 0.01. The test statistic is Type an integer or a decimal.) The p-value is Type an integer or a decimal.) Draw a conclusion. Choose the answer below A. B. C. D. Do not reject the null hypothesis. There is sufficient evidence to support the alternative hypothesis. Do not reject the null hypothesis. There is not sufficient evidence to support the alternative hypothesis. Reject the null hypothesis. There is not sufficient evidence to support the alternative hypothesis. Reject the null hypothesis. There is sufficient evidence to support the alternative hypothesis Use a 95% confidence interval to estimate β2 (Round to three decimal places as needed.) f. Find R? and R2 and interpret these values. R2 sample size and the number of Bparameters in the model. % indicates the percentage of the total sample va ation o the y values accounted or by the model Ra- 9 indicates the percentage o he va ation n y alues accounted or hemod ad uste the (Type integers or decimals.) g. Find the test statistic for testing Ho β,-P2-0. The test statistic is Type an integer or a decimal.) h.Find the observed significance level of the test in part g Interpret the result The observed significance level is Type an integer or a decimal.)

Answer 1

solving first four sub-parts by HomeworkLib policy

a)
b0^ = 1738.93
b1^ = -384.54
b2^ = -517.39

b)
y^ = 1738.93 -384.54 x1 -517.39 x2

c)

SSE = 502948
MSE = 29585
s = sqrt(MSE) = sqrt(29585) = 172.0029

predict future values of y for given values of x
thus it would be expected ... predcitons of y to with about 2 s = 2*172.003 = 344.006

d)
TS = -3.78
p-value = 0.002
p-value < alpha
hence we reject the null hypothesis

option D) is correct