Question

A consumer analyst collected the following data on the screen sizes of popular LCD televisions sold recently at a large retailer: Manufacturer Screen Price Sharp 28 $1,425.00 Samsung 42 2,727.00 Samsung 46 3,025.00 Sony 32 1,412.50 Sharp 31 2,319.50 Samsung 28 1,061.50 Samsung 28 1,165.00 Sharp 48 2,853.50 Sharp 31 1,737.50 Sony 51 2,194.00 Sony 44 2,332.50 Samsung 52 2,955.00 Sharp 32 1,395.00 Sharp 46 2,355.00 Sharp 26 880.00 Samsung 34 1,490.50 Sharp 36 1,369.00 Samsung 39 2,250.00 Sony 28 1,035.00 Sony 38 1,615.00 Sony 54 2,471.00 Sony 44 2,066.00 Sony 26 1,050.00 PictureClick here for the Excel Data File a. Does there appear to be a linear relationship between the screen size and the price? (Round your answer to 2 decimal places.) , The correlation of Screen and Price is . b. Which variable is the "dependent" variable? c-1. Use statistical software to determine the regression equation. (Negative amounts should be indicated by a minus sign. Round your answers to the nearest whole number.) Price = + Screen. c-2. Interpret the value of the slope in the regression equation. For each inch in screen size, the price increases $ on average. d. Include the manufacturer in a multiple linear regression analysis using a "dummy" variable. Does it appear that some manufacturers can command a premium price? Hint: You will need to use a set of indicator variables. (Round your answers to 2 decimal places. Negative amounts should be indicated by a minus sign.) Price = + Screen + Manufacturer Sharp + Manufacturer Sony e. Test each of the individual coefficients to see if they are significant. (Round your answers to 2 decimal places. Leave no cells blank - be certain to enter "0" wherever required. Negative amounts should be indicated by a minus sign.) Predictor T P Constant Screen Manufacturer_Sharp Manufacturer_Sony

Answer 1

a)

simple linear regression

model <- lm (Price~Screen,data=data)
> summary(model)

Call:
lm(formula = Price ~ Screen, data = data)

Residuals:
   Min     1Q Median     3Q    Max 
-539.1 -227.4 -103.5  218.1  860.0 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept) -514.418    329.790  -1.560    0.134    
Screen        63.676      8.544   7.453 2.52e-07 ***
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 363.7 on 21 degrees of freedom
Multiple R-squared:  0.7256,    Adjusted R-squared:  0.7126 
F-statistic: 55.54 on 1 and 21 DF,  p-value: 2.516e-07

correlation = 0.8518

there appears to be linear relation between screen size and price

b)

price is dependent variable

c) 1) y^= -514.418 + 63.676 Screen

c2) slope = 63.676

when screen size increases by 1 unit, on average price increases by 63.676 units

d)

Multiple regression

model2 <- lm (Price~Screen+Manufacturer,data=data)

summary(model2)

Call:
lm(formula = Price ~ Screen + Manufacturer, data = data)

Residuals:
    Min      1Q  Median      3Q     Max 
-506.08 -247.58    2.57  182.33  777.48 

Coefficients:
                  Estimate Std. Error t value Pr(>|t|)    
(Intercept)       -463.505    330.132  -1.404   0.1765    
Screen              66.612      7.958   8.370  8.5e-08 ***
ManufacturerSharp  -59.437    172.770  -0.344   0.7346    
ManufacturerSony  -403.982    170.538  -2.369   0.0286 *  
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 329 on 19 degrees of freedom
Multiple R-squared:  0.7968,    Adjusted R-squared:  0.7648 
F-statistic: 24.84 on 3 and 19 DF,  p-value: 8.673e-07

y^= -463.505 + 66.612 Screen -59.437 Manufacturer Sharp -403.982 ManufacturerSony