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Concept explainers
The Tire Rack, an online distributor of tires and wheels, conducts extensive testing to provide customers with products that are right for their vehicle, driving style, and driving conditions. In addition, The Tire Rack maintains an independent consumer survey to help drivers help each other by sharing their long-term tire experiences (The Tire Rack website, August 1, 2016). The following data show survey ratings (1 to 10 scale with 10 the highest rating) for 18 high-performance all-season tires. The variable Tread Wear rates quickness of wear based on the driver’s expectations, the variable Dry Traction rates the grip of a tire on a dry road, the variable Steering rates the tire’s steering responsiveness, and the variable Buy Again rates the driver’s desire to purchase the same tire again.
- a. Develop an estimated simple linear regression equation that can be used to predict the Buy Again rating given the Tread Wear rating. At the .01 level of significance, test for a significant relationship. Does this estimated regression equation provide a good fit to the data? Explain.
- b. Develop an estimated multiple regression equation that can be used to predict the Buy Again rating given the Tread Wear rating and the Dry Traction rating. Is the addition of the Dry Traction independent variable significant at α = .01? Explain.
- c. Develop an estimated multiple regression equation that can be used to predict the Buy Again rating given the Tread Wear rating, the Dry Traction rating, and the Steering rating. Is the addition of the Steering independent variable significant at α = .01? Explain.
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Chapter 15 Solutions
Bundle: Modern Business Statistics with Microsoft Office Excel, Loose-Leaf Version, 6th + MindTap Business Statistics, 2 terms (12 months) Printed Access Card
- A well-known company predominantly makes flat pack furniture for students. Variability with the automated machinery means the wood components are cut with a standard deviation in length of 0.45 mm. After they are cut the components are measured. If their length is more than 1.2 mm from the required length, the components are rejected. a) Calculate the percentage of components that get rejected. b) In a manufacturing run of 1000 units, how many are expected to be rejected? c) The company wishes to install more accurate equipment in order to reduce the rejection rate by one-half, using the same ±1.2mm rejection criterion. Calculate the maximum acceptable standard deviation of the new process.arrow_forward5. Let X and Y be independent random variables and let the superscripts denote symmetrization (recall Sect. 3.6). Show that (X + Y) X+ys.arrow_forward8. Suppose that the moments of the random variable X are constant, that is, suppose that EX" =c for all n ≥ 1, for some constant c. Find the distribution of X.arrow_forward
- 9. The concentration function of a random variable X is defined as Qx(h) = sup P(x ≤ X ≤x+h), h>0. Show that, if X and Y are independent random variables, then Qx+y (h) min{Qx(h). Qr (h)).arrow_forward10. Prove that, if (t)=1+0(12) as asf->> O is a characteristic function, then p = 1.arrow_forward9. The concentration function of a random variable X is defined as Qx(h) sup P(x ≤x≤x+h), h>0. (b) Is it true that Qx(ah) =aQx (h)?arrow_forward
- 3. Let X1, X2,..., X, be independent, Exp(1)-distributed random variables, and set V₁₁ = max Xk and W₁ = X₁+x+x+ Isk≤narrow_forward7. Consider the function (t)=(1+|t|)e, ER. (a) Prove that is a characteristic function. (b) Prove that the corresponding distribution is absolutely continuous. (c) Prove, departing from itself, that the distribution has finite mean and variance. (d) Prove, without computation, that the mean equals 0. (e) Compute the density.arrow_forward1. Show, by using characteristic, or moment generating functions, that if fx(x) = ½ex, -∞0 < x < ∞, then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed random variables.arrow_forward
- 1. Show, by using characteristic, or moment generating functions, that if 1 fx(x): x) = ½exarrow_forward1990) 02-02 50% mesob berceus +7 What's the probability of getting more than 1 head on 10 flips of a fair coin?arrow_forward9. The concentration function of a random variable X is defined as Qx(h) sup P(x≤x≤x+h), h>0. = x (a) Show that Qx+b(h) = Qx(h).arrow_forward
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