Consumer Reports tested a number of different point-and-shoot cameras. They developed a score based

upon factors such as the number of megapixels, weight (oz), image quality, and ease of use. The score ranges

from 0 to 100, with higher scores indicating better overall results. For consumers, selecting a camera can be a

difficult task, considering the wide-ranging number of options, variations in price, and the number of

megapixels. In order to help address some of these concerns, they developed a model to determine, among

other things, whether a camera with more megapixels scores higher, or if more expensive cameras scored higher

than inexpensive ones. Data was collected on 51 cameras from two brands: 23 Nikon and 28 Canon.

NOTE: For those unfamiliar with the terminology, "Megapixel" is a measure of the number of pixels (tiny dots)

that make up the image produced by a digital camera. More pixels typically correspond to a higher quality,

higher resolution, more detailed image.

The model takes the following form:

= ( + "" + !! + ## + $$ +

Where " is a dummy variable for brand using Canon as the reference case, ! is price ($), # is number of

megapixels (MP) and $ is weight (oz).

The results of the estimation along with a standardized residual plot are on the last page of the exam. All testing

is done at = 0.05 level of significance.

a) Write the estimated regression equation.

b) Interpret the estimated coefficients on brand and price.

c) Interpret the interval estimates of the coefficients on brand and megapixels.

c) Interpret the adjusted R-square.

d) Is the model statistically significant? Explain.

e) Are the independent variables statistically significant? Explain. (Be concise, can discuss as a group)

f) Do you have any reason to believe there may be a problem with multicollinearity? Explain.

g) Evaluate the standardized residual plot and suggest any necessary revisions to the model.

h) What would it mean to commit a Type I error for the t-test on price?

i) What would be the predicted score for a $250, 13MP, Nikon camera that weights 5oz?

SUMMARY OUTPUT

Regression Statistics

Multiple R 0.77

R Square 0.60

Adj R Square 0.56

Standard Error 5.21

Observations 51

ANOVA

df SS MS F p-value

Regression 4 1,868.76 467.19 17.21 0.00

Residual 46 1,249.01 27.15

Total 50 3,117.77

Coefficients Standard Error t Stat P-value Lower 95% Upper 95%

Intercept 44.63 4.15 10.76 0.00 36.28 52.98

Brand -6.71 1.49 -4.50 0.00 -9.71 -3.71

Price ($) 0.05 0.01 4.54 0.00 0.03 0.07

Megapixels 0.54 0.25 2.18 0.03 0.04 1.04

Weight (oz.) -0.07 0.36 -0.19 0.85 -0.80 0.66