statistics help An investigator is interested in the effect of distance (in mile
ID: 3223416 • Letter: S
Question
statistics help
An investigator is interested in the effect of distance (in miles) on airfare prices (in dollars) for the DTW flights. He collects the average prices for 14 different destinations in order to build a linear regression model. Based on the following Minitab output, answer the questions: The regression equation is price = beta_0 + beta_1 distance "SE Coef' column contains the standard deviations of estimations for beta_0 and beta_1. a. What is the equation for the estimated regression model? b. Does the simple linear regression model specify a useful relationship between distance and price? Use the appropriate test procedure on the slope and then reach a conclusion at significance level 5%. c. Calculate r^2. d. Using the context of the problem, interpret the slope and the intercept of the linear regression line. e. If y = 417.9, calculate the 95% prediction interval for a future Y observation to be made when x = 1000.Explanation / Answer
a) Price = 186.8 + .20652* Distance
b) We can use p-value method. If the slope coefficient is significant, then the regression model is useful/valid.
At a 95% level or p=.05, conduct hypothesis as follows
H0: Slope coefficient = 0
H1: Slope coefficient not 0
From the minitab output, p = .01 and since p < critical p (=.05), we reject NULL and conclude that the slope
coefficient is significant
c) r2 = SSR/SST where SSR is Sum Sq Regression and SST is Total Sum of Sq
= 320799/727141
= .4411
d) Intrepretation of slope is that for additional mile, the price of ticket increases by $.20652
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