Question

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). Click on the datafile logo to reference the data DATA file Brand & Model Samsung Ultrabook NP900X3C-A0IUS Apple MacBook Air MC965LL/A Apple MacBook Air MD23ILLA HP ENVY 13-2050nr Spectre XT Sony VAIO SVS13112FXB Acer Aspire 55-391-9880 Ultrabook Apple MacBook Pro MDIOILLA Apple MacBook Pro MD313LLJA Dell Inspiron 113Z-6591SLV Samsung NP535U3C-AOIUS Price ($) 1250 1300 1200 950 800 1200 1200 1000 700 600 Overall Score 83 83 82 79 77 74 74 73 63 a. Select a scatter diagram with price as the independent variable. 85 1 80 75 70 Overall Score 65 65 60 55 50 400 600 800 1200 1400 1000 Price (S)

Answer 1

a)

The correct scatter diagram is fig 3

85 80 75 70 Overall Score 65 60 55 50 400 600 1200 1400 800 1000 Price ($)

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b)

The scatter diagram indicate that the relationship between price and overall score is

direct

which means the overall score increases, as the price increases and vice versa.

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c)

Regression equation is determined using least squares method as below

X 1250 1300 1200 950 800 1200 1200 1000 700 600 10200 83 83 82 79 77 74 74 73 67 63 755 x*y 103750 107900 98400 75050 61600 88800 88800 73000 46900 37800 782000 1562500 1690000 1440000 902500 640000 1440000 1440000 1000000 490000 360000 10965000 x = Price $ (Independent variable) y = Overall Score (dependent variable) N= Σx = Σy = 10 10200 755 Σx = (Σx) = Σχy = 10965000 1.04E+08 782000 Slope (b) = 0.0212 (Ν ΣΧΥ - ΣΧΣΥ) - Ν Σx - (Σκ)? Intercept (a) = 53.876 (Σy - bΣx) = N Regression Equation: y = 53.876 + 0.0212x

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d)

Slope of the regression equation is 0.0212

Interpretation of slope: It means that overall score increases by 0.0212 points for every dollar increase in price

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e)

Overall score is predicted by substituting the value of x=700 in the regression equation

Predicted overall score (y) = 53.876+0.0212*700

= 68.7

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