Question

DATAe: Computer 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, dsplay, 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. Overal Score Brand & Model Price ($) Samsung Ultrabook NP900X3C-A01us 1,250 83 Apple MacBook Air MC965LL/A 1,300 83 Apple MacBook Air MD231LL/A 1,200 82 HP ENVY 13-2050nr Spectre XT 950 79 Sony VAIO SVS13112FXB 800 77 Acer Aspire S5-391-9880 Ultrabook 1.200 74 Apple MacBook Pro MD101LL/A. 1.200 74 Apple MacBook Pro MD313LL/A 1,000 73 Dell Inspiron 1132z-6591SLV 700 67 Samsung NP535U3C-A01US 600 61 (a) Develop a scatter diagram with price as the independent variable 85- 85- 85- 80- 80- 80 e754 734 y75 20- 70 654 65 65- 60- 55 55- 55 600 600 800 800 1000 1200 1400 1000 1200 1400 400 800 1000 1200 1400 ..

Answer 1

Solution:

We have the following R code to find the scatter plot of Price and Overall Score:

Price<-c(1250,1300,1200,950,800,1200,1200,1000,700,600)
Score<-c(83,83,82,79,77,74,74,73,67,63)
plot(Price, Score,xlab="Price",ylab="Score", main="Scatter PLot")

The output is the following:

Scatter PLot 80 70 600 700 800 900 1000 1100 1200 1300 Price Score

Part(a) The correct answer is: (c)

85- 804 2 75- 70 65 8 60. 55 800 1000 1200 1400 600 Price (5)

Part(b) The relationship the Scatter Diagram indicates between the two random variables is:

(a) There appears to be a positive relationship between Price($) and Overall Score.

Because as, Price Increases the Overall Score also increases.

Part(c) The R code for finding the regression equation is:

> Relation<-lm(Score~Price)
> summary(Relation)

Call:
lm(formula = Score ~ Price)

Residuals:
Min 1Q Median 3Q Max
-5.3182 -3.2121 -0.0758 2.6667 6.1667

Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 53.863636 6.175123 8.723 2.33e-05 ***
Price 0.021212 0.005897 3.597 0.00701 **
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 4.417 on 8 degrees of freedom
Multiple R-squared: 0.6179,   Adjusted R-squared: 0.5702
F-statistic: 12.94 on 1 and 8 DF, p-value: 0.007013

Here, the intercept is 53.864 and the regression coefficient of Score on Price is 0.021.

The regression equation is:

$\hat{y}=53.864-0.021x,\ where\ \hat{y}= \ predicted\ overall\ score \ and\ x=Price(\$ \)$

Part(d) The correct interpretation is the following:

(b) The slope gives the change in the overall score for every one dollar increase in price.

Part(e) We put $x=\$950$ in the regression equation and get,

$\hat{y}=53.864-0.021*950=33.914\simeq 34.0$

The predicted overall score when the price is 950$ is = 34.0 .