Question

1) 14.11, part c (regression equation)

2) 14.11, part e

11. To help consumers in purchasing a laptop computer, Consumer Reports calculates an overall test score for each computer tested based upon rating factors such as ergonomics, portability, performance, display, and battery life. Higher overall scores indicate better test results. The following data show the average retail price and the overall score for ten 13-inch models (Consumer Reports website, October 25, 2012) DATA Brand & Model Price (S) Overall Score Samsung Ultrabook NP900X3C-A01US Apple MacBook Air MC965LLIA Apple MacBook Air MD231LLA HP ENVY 13-2050nr Spectre XT Sony VAIO SVS13112FXB Acer Aspire S5-391-9880 Ultrabook Apple MacBook Pro MD101LLIA Apple MacBook Pro MD313LLIA Dell Inspiron 113Z-6591SLV Samsung NP535U3C-A01US 1250 83 1300 83 1200 82 950 79 800 77 1200 74 1200 74 1000 73 700 67 600 63 a. Develop a scatter diagram with price as the independent variable b. What does the scatter diagram developed in part (a) indicate about the relationship between the two variables? c. Use the least squares method to develop the estimated regression equation. d. Provide an interpretation of the slope of the estimated regression equation. e. Another laptop that Consumer Reports tested is the Acer Aspire S3-951-6646 Ultrabook; the price for this laptop was $700. Predict the overall score for this laptop using the estimated regression equation developed in part (c)

Answer 1

1.

Sum of X = 10200
Sum of Y = 755
Mean X = 1020
Mean Y = 75.5
Sum of squares (SS_X) = 561000
Sum of products (SP) = 11900

Regression Equation = ŷ = bX + a

b = SP/SS_X = 11900/561000 = 0.0212

a = M_Y - bM_X = 75.5 - (0.02*1020) = 53.8636

ŷ = 0.0212X + 53.8636

2. For x=700,

ŷ = 0.0212*700 + 53.8636=68.7036