'Consumer Reports' is an American magazine published monthly by Consumer Reports (a spin-off company created in 2012) since 1936. It publishes reviews and comparisons of consumer products and services based on reporting; and results from its in-house testing laboratory and survey research center. In 2012, Consumer Reports tested 166 different point-and-shoot digital cameras. A number of variables were measured including number of megapixels, weight (in ounces), and price (in American dollars). They developed an overall quality score based on these and other variables (e.g. ease of use and image quality). The overall quality score ranged from 0 to 100, with higher scores indicating better overall test results.
A random sample of 28 point-and-shoot digital cameras was tested. This data set is available in 'MS Excel' format (filename: camera.xlsx) and it can be accessed from the 'Data Sets' module through our course homepage on D2L. The record structure of this data set is summarized below.
VARIABLE | COLUMN
Observation (element) number | A
Brand | B
Price (US dollars) | C
Number of megapixels | D
Weight (in ounces) | E
Overall quality score (out of 100) | F
Question #1
(a) Using 'overall quality score' as the dependent variable, construct scatter diagrams for the following independent variables: (a) weight, (b) number of megapixels and (c) price. Which of these independent variables appears to be the best predictor of overall score? Explain your choice. Describe the features of the scatter diagram for your chosen 'independent' variable. [10 marks]
(b) Is there a statistically significant linear relationship between 'overall quality score' and your chosen independent variable? Support your answer by carrying out the four steps of hypothesis testing to assess the statistical significance of 'r'. [4 marks]
(c) Obtain the equation of the estimated least squares regression line. Provide an interpretation of the estimated slope in context. [3 marks]
(d) Predict the 'overall quality score' for a camera that has a price of (a) $250 and (b) $350. What is the difference in predicted 'overall quality score' between a $350 and $250 camera? [3 marks]