HW: Statistical Inferences Assignment

Note: This assignment uses the exact same three datasets as the previous assignment. Also similar to the previous assignment, most questions are near identical (primary differences exist in parts f and g).

x y

56.1849011143672943.969674041229

64.15068787325831000.47558001509

56.161364956165901.596812402055

25.59280534182341055.41992065146

51.1290969113663923.809002623309

36.9524465188427879.808374683292

51.2090408241569803.703204591687

78.1615248428741854.672286828961

16.9998416214335925.122038249344

75.1535740049024858.090873356225

24.801979109722895.530974257285

30.38763577536441013.9676797885

69.8326367319302883.063102016308

16.5929919412267927.645784463128

84.9163023103808814.569424981026

58.3705016925152831.487087581704

55.42152756933151078.36635754037

55.8158329153472943.940207883983

74.797311335765639.545690391107

92.491368579185794.148096275552

79.7205366271925717.738481441503

54.0735554981555818.052218848214

25.6442092697707985.237370388419

43.704445862777896.448704409173

76.8848379152888809.329431682585

65.6724432384336809.34962329774

40.7875126775062979.224631298056

37.2123417692922903.774582336936

102.4845407531781011.31353316366

14.4841250386032788.130278129214

24.1193377823916830.244798634745

61.6749534486014966.465498548724

58.6465055311874878.265038039133

48.5262318619122942.394306346132

37.6233455463753986.130711403465

54.8556236064774884.040385773202

46.1785908573591756.881885627676

56.3985920868098882.827021039806

32.1981164012445863.094224117266

79.877905500073880.952030815311

63.3744623575006960.693238859104

40.06534599518061021.41463866466

74.8325929977092835.640598466971

62.3910737096706798.392035279932

63.35388835659981096.39274996473

43.4942987007385890.749815978485

31.1380326335749934.087557441466

71.5661368363749751.731854105538

65.4959891262279973.662745892727

52.91011010099331068.07210376183

Q2: For Dataset 2, use appropriate R functions, including lm, to provide the requested information.

a) What is the MSRes (note: the sigma function in R gives the square root of the MSRes for a linear model data frame)

b) We wish to test the following hypotheses at the 95% confidence level

H0: \beta 0=0 vs. H1: \beta 0!=0.

i) What conclusion is drawn regarding H0?(Highlight answer) Reject Fail to reject

ii) What is the associated p value?

c) We wish to test the following hypotheses at the 95% confidence level

H0: \beta 1=0 vs. H1: \beta 1!=0.(This is also the significance of the regression, as we only have one regressor)

i) What conclusion is drawn regarding H0?(Highlight answer) Reject Fail to reject

ii) What is the associated p value?

d) What is the confidence interval for \beta 0?

e) What is the confidence interval for \beta 1?

f) What is the confidence interval for E(Y|x)=\mu Y|x if x =40?

g) What is the prediction interval for Y if x =40?