Question

Student ID: Question 1 Given are five observations for two variables, x and y. xi yi 2 25 3 25 5 20 1 30 8 16 a. Develop the regression equation by computing the values of βˆ 0 and βˆ 1. b. Use the estimated regression equation to predict the value of y when x = 6. c. Compute SSE, SST, and SSR. d. Compute the coefficient of determination r 2 . Comment on the goodness of fit. e. Compute the sample correlation coefficient. f. Compute the mean square error (MSE). g. Compute the standard error of the estimate. h. Compute the estimated standard deviation of βˆ 1. i. Use the t-test to test the following hypotheses at the 5% significance level: H0 : β1 = 0 H1 : β1 6= 0 Is β1 significant at the 5% level? j. Construct a 99% confidence interval for β1

Answer 1

a

b)

predicted value =30.331+(-1.877)*6=19.069

c)

SSE =(SSx*SSy-SSxy²)/SSx =6.3312

SST =SSy=114.80

SSR =SST-SSE =108.469

d)

coefficient of determination r² =SSR/SST =0.9449

as coeffiicent of determination is very high, regression fit is very good.

e)

sample correlation coefficient =SSxy/sqrt(SSx*SSy)=-0.9720

f)mean square error (MSE)=SSE/(n-2)=2.1104

g)

standard error of the estimate se =sqrt(MSE)=1.4527

h)

estimated standard deviation sb1 =se/sqrt(SSxx)=0.2618

i)

as test statistic is in crtiical region we reject null hypothesis

we have sufficient evidence to conclude that slope is signfiicant

j)

for 99 % CI value of t=					5.8410
margin of error E=t*std error                            =					1.5289
lower confidence bound=estimated slope-margin of error =					-3.41
Upper confidence bound=estimated slope+margin of error=					-0.35