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
- Q: The dataset posted below lists a sample of months and the advertising budget (in hundreds of dollars) for TV, radio and newspaper advertisements. Also included is whether a coupon was published for that month and the resulting sales (in thousands of dollars). a) Develop a multiple regression model predicting the sales based off the four predictor variables: TV, radio, and newspaper advertising budget and whether a coupon is used. Recode Coupon as 0 = No and 1 = Yes. Report the estimated regression equation (Solve in Excel) TV ($100) radio ($100) newspaper ($100) Coupon sales ($1000) 0.7 39.6 8.7 No 1.6 230.1 37.8 69.2 No 22.1 4.1 11.6 5.7 Yes 3.2 44.5 39.3 45.1 No 10.4 250.9 36.5 72.3 No 22.2 8.6 2.1 1 No 4.8 17.2 45.9 69.3 Yes 9.3 104.6 5.7 34.4 No 10.4 216.8 43.9 27.2 Yes 22.3 5.4 29.9 9.4 No 5.3 69 9.3 0.9 No 9.3 70.6 16 40.8 No 10.5 151.5 41.3 58.5 No 18.5 195.4 47.7 52.9 Yes 22.4 13.1 0.4 25.6 Yes 5.3 76.4 0.8…arrow_forwardA 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_forwardSam Jones has 2 years of historical sales data for his company. He is applyingfor a business loan and must supply his projections of sales by month for thenext 2 years to the bank. a. Using the data from Table 6–12, provide a regression forecast for timeperiods 25 through 48.b. Does Sam’s sales data show a seasonal pattern?arrow_forward
- I would need some assistance with problem nineteen, please?arrow_forwardTen cars between 1 and 6 years old were randomly selected from the classified ads. The data were obtained, where x denotes age, in years, and y denotes price, in hundreds of dollars. Develop a scatterplot and describe the relationship between the price and the age of the cars. b) Find and interpret the correlation coefficient. c) d) At 5% level, test whether the age and the price of the cars are linearly related. D Find the regression equation and interpret the regression coefficients.arrow_forwardFind the new data point (x,y) in which x=2 from the data points (1.3) and (4.12)arrow_forward
- Consider the following five data points: X -1 0 1 2 3 Y -1 1 2 4 5 a. Use regression analysis to calculate by hand the estimated coefficients of the equation Y = B + aX. b. Compute the standard error and the t-statistics for the coefficient of X.arrow_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_forwardc) 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_forward
- 7. Find slop of a linear regression model for the following data: x = [1, 2, 3, 4, 5, 6, 7] z = [ 1.40, 3.78, 4.41, 4.60, 8.40, 8.64, 12.81]. -1.7 -0.5 0.5 O 1.7 CS Scanned with CamScannelarrow_forward2arrow_forwardWhich non-parametrical test for ordinal data is the best use in the given scenario? In a study by Grape et. al, researchers investigated the possible beneficial effects of singing on well-being during a single singing lesson. One of the variables of interest was the change in cortisol as a result of the singing lesson. Use the data in the following table to determine if, in general, cortisol increases after a singing lesson. Let a = 0.05. Find the p value. Subject 1 2 3 4 5 6 7 8 Before 214 362 202 158 403 219 307 331 After 232 276 224 412 562 203 340 313 a. Kruskal-Wallis Test b. Sign Test c. Spearman and Kendall Correlation Coefficients d. Wilcoxon Rank Sum Test e. Mood Median Test f. Wilcoxon Matched-Pairs Signed-Ranks Testarrow_forward
- Functions and Change: A Modeling Approach to Coll...AlgebraISBN:9781337111348Author:Bruce Crauder, Benny Evans, Alan NoellPublisher:Cengage Learning