Concept explainers
The article “The Analysis and Selection of Variables in Linear Regression” (Biometrics [1976]: 1–49) reports on an analysis of data taken from issues of Motor Trend magazine. The dependent variable y was gas mileage and there were n = 32 observations. The independent variables were x1 = Engine type (1 = straight, 0 = V), x2 = number of cylinders, x3 = Transmission type (1 = manual, 0 = automatic), x4 = Number of transmission speeds, x5 = Engine size, x6 = Horsepower, x1 = Number of carburetor barrels, x8 = Final drive ratio, x9 = Weight, and x10 = Quarter-mile time. The R2 and adjusted R2 values are given in the accompanying table for the best model using k predictors for k = 1,…, 10.
Which model would you select? Explain your choice and the criteria used to reach your decision.
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Chapter 14 Solutions
Introduction to Statistics and Data Analysis
- A statistical program is recommended. Car manufacturers produced a variety of classic cars that continue to increase in value. Suppose the following data is based upon the Martin Rating System for Collectible Cars, and shows the rarity rating (1–20) and the high price ($1,000) for 15 classic cars. (b) Develop an estimated multiple regression equation with x = rarity rating and x2 as the two independent variables. (Round b0 and b1 to the nearest integer and b2 to one decimal place.) (c) Consider the nonlinear relationship shown by equation (16.7): E(y) = β0β1x Use logarithms to develop an estimated regression equation for this model. (Round b0 to three decimal places and b1 to four decimal places.)arrow_forwardThe table contains data on vehicle speed (h) and fuel consumption (lt / 100km) of 5 randomly selected vehicles. Estimate the average fuel consumption of a vehicle traveling at 45 km / h using the simple linear regression equation between vehicle speed and fuel consumption. Speed 55 60 65 70 75 Consumption 11 10 9 8 7 Please choose one: a. 6 b. 5 c. 13 D. 8arrow_forwardFind the new data point (x,y) in which x=2 from the data points (1.3) and (4.12)arrow_forward
- The following scores represent a nurse’s assessment (X) and a physician’s assessment (Y) of the condition of 10 patients at time of admission to a trauma centre: X: 18 13 18 15 10 12 8 4 7 3 Y: 23 20 18 16 14 11 10 7 6 4 a) Obtain the regression equation. b) What is the predicted physician’s assessment for a nurse’s assessment of; 16 scores? 21 scores? c) Distinguish between extrapolation and interpolationarrow_forwardExplain the slope of the regression line when predicting Y from X? X Y 13 11 7 7 11 11 6 7 8 10 10 9 9 9 11 10 12 12 8 11 6 7 9 9 8 7 11 8 11 12 8 7 8 9 6 8 8 13 9 10 8 6 11 9 11 11 1 8 9 5arrow_forwardWould I use the regression line to predict Y from X ? And what is the pattern of the scatterplot?arrow_forward
- c) Show that the coefficient of determination, R², can also be obtained as the squared correlation between actual Y values and the Y values estimated from the regression model where Y is the dependent variable. Note that the coefficient of correlation between Y and X is Eyixi r = And also that ỹ = ŷ (18.75)arrow_forward2arrow_forwardThe following is the result of the multiple linear regression analysis in STATISTICA, where the response Y = lung capacity of a person, xage = age of the person in years, xheight = height of the person in inches, = a categorical variable with 2 levels (0 = non- X smoke smoker, 1 = smoker), and xCaesarean = a categorical variable with 2 levels (0 = normal delivery, 1 = %3D %3D Caesarean-section delivery). b* Std.Err. Std.Err. t(720) p-value N=725 Intercept Age Height Smoke Caesarean of b 0.467772 0.017626 of b* -11.8001 0.1372 0.2790 -0.6407 -25.2263 7.7846 28.6552 -5.0142 0.000000 0.000000 0.000000 0.206427 0.026517 0.026340 0.754765 -0.074205 -0.033054 0.009735 0. 127774 0.092146 0.000001 0.022851 0.014799 0.014492 -0.2102 -2.2808 What is the predicted lung capacity of an 14-year old non-smoker whose height is 71 inches born by normal delivery? (final answer to 4 decimal places)arrow_forward
- A researcher wants to study the factors affecting a person's decision to buy a car. For his study, he selects a random sample of 100 people from a city and estimates the following regression equation: C = - 7.35 + 0.44/+ 0.36M – 0.27P, where C is a binary dependent variable which denotes the decision to buy the car (C equals 1 if the person decides to buy the car, and 0 otherwise), / denotes the monthly income of the person (I equals 1 if the income exceeds $5,000 and 0 otherwise), M denotes the car's mileage (measured in miles per gallon) and P denotes the price of the car (in thousand dollars). The researcher wants to test the hypothesis that the coefficient on /, B4, and the coefficient on M, B2, are jointly zero, against the hypothesis that at least one of these coefficients is non-zero. The test statistics for testing the null hypotheses B1 =0 and B = 0 are calculated to be 1.55 and 1.25, respectively. Suppose that these test statistics are uncorrelated. The F-statistic associated…arrow_forward2) Use the given information to find the coefficient of determination. A regression equation is obtained for a collection of paired data. It is found that the total variation is 20.711, the explained variation is 18.592, and the unexplained variation is 2.119. A) 1.114 B) 0.102 C) 0.898 D) 0.114arrow_forwardThis dataset continues our saga of modeling the price of this popular Honda automobile. The dataset has now been cleaned to remove the columns with the dealership where the car was offered for sale and specific trim. (a) write out your model in econometric notation. Be very precise! (b) using the 93 observations in the dataset, estimate a model where price is a function of age, mileage and trim of the car. Be sure to avoid the dummy variable trap!! Fully report the results of your model. In this case, interpretation of the coefficients on the dummy variables is particularly important. (c) test the hypothesis that the specific trim does not affect the price of a Civic. Be sure to do all parts of the hypothesis test. (please fully describe steps if you are using Excel) Price Years Old KM EX EXT SE Sport Touring 6555 9 290363 0 0 0 0 0 9999 9 142258 0 0 0 0 0 10281 6 132644 0 0 0 0 0 12480 5 167125 0 0 0 0 0 12991 7 57398 0 0 0 0 0 12991 6 93046 0 0 0 0 0 12991…arrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning