attachments_bde86cb143d6be01439acef1117fd6a41c114f18 Pres Temp 20.79 194.5 20.79 194.3 22.4 197.9 22.67 198.4 23.15 199.4 23.35 199.9 23.89 200.9 23.99 201.1 24.02 201.4 24.01 201.3 25.14 203.6 26.57 204.6 28.49 209.5 27.76 208.6 29.04 210.7 29.88 211.9 30.06 212.2 Page 1 Problem 5. (10 points) A national insurance organization wanted to study the consumption pattern of cigarettes in all 50 states and the District of Columbia. The variables chosen for the study are: 0 Age: Median age of a person living in a state. a HS: Percentage of peeple over 25 years of age in a state who had completed high school. 0 Income: Per capita personal income for a state (income in dollars). 0 Black: Percentage of blacks living in a state. a Female: Percentage of females living in a state. 0 Price: Weighted average price (in cents) of a pack ofcigarettes in a state. 0 Sales: Number of packs of cigarettes sold in a state on a per capita basis. The data can be found at http : / /www1 . aucegypt . edu/ f aculty/ hadi/ RABE5/ Data5/ P088 . txt Below, specify the null and alternative hypotheses, the test used, and your conclusion using a 5% level of signicance. (a) (3 points) Test the hypothesis that the variable Female is not needed in the regression equation relating Sales to the six predictor variables. (b) (3 points) Test the hypothesis that the variables Female and HS are not needed in the above regression equation. (c) (2 points) Compute a 95% condence interval for the true regression coefcient of the variable Income. (d) (2 points) What percentage of the variation in Sales can be accounted for when Income is removed from the full model? Problem 6. (10 points) Consider the linear model K; 2 g + lm + 5,; for z" = 1, . . . , n and assume all the three assumptions on ei's as discussed in class. Suppose a new observation mn+1 arrives while its response yn+1 2 g + lm.\" + an\" is unseen. Assuming 6\".\" has the same distribution as ei's, we are interested in constructing condence intervals for yn+1 and its average g + 1$n+1. 4 HOMEWORK 5 (a) (2 points) Show that o + les.\" is unbiased for estimating g + lwnH. (b) (3 points) Briey explain why g +1xn+1 has a normal distribution, and prove that its variance is given as 02 1 M n Sm Here, :3 = (:31 + - - - + xn)/n. (c) (3 points) Give a 1 a condence interval for o + lxn+1. (d) (2 points) Give a 1 a condence interval for yn+1. This is called the prediction interval for an\". Problem 7. (5 points) The le alps. csv contains data on the barometric pressure (in inches of mercury) and the boiling point (in F) of water in the Alps. (a) (2 points) Make a scatter plot of the boiling point by barometric pressure. Fit a least squares regression line. Report the result. What preportion of variation in the boiling point is accounted for by linear regression on the barometric pressure? (b) (3 points) Calculate a 95% CI for the boiling point if the barometric pressure is 28 inches of mercury. Interpret your Cl. (Hint: the R function predict is helpful here.)