1 views Consumer Reports tested 166 different point-and-shoot digital cameras. Based upon factors such as the number of megapixels, weight (oz.), image quality, and ease of use, they developed an overall score for each camera tested. The overall score ranges from 0 to 100, with higher scores indicating better overall test results. Selecting a camera with many options can be a difficult process, and price is certainly a key issue for most consumers. By spending more, will a consumer really get a superior camera? And, do cameras that have more megapixels, a factor often considered to be a good measure of picture quality, cost more than cameras with fewer megapixels? Table 14.13 shows the brand, average retail price ($), number of megapixels, weight (oz.), and the overall score for 13 Canon and 15 Nikon subcompact cameras tested by Consumer Reports (Consumer Reports website). Managerial Report 1. Develop numerical summaries of the data. 2. Using overall score as the dependent variable, develop three scatter diagrams, one using price as the independent variable, one using the number of megapixels as the independent variable, and one using weight as the independent variable. Which of the three independent variables appears to be the best predictor of overall score? 3. Using simple linear regression, develop an estimated regression equation that could be used to predict the overall score given the price of the camera. For this estimated regression equation, perform an analysis of the residuals and discuss your findings and conclusions. 4. Analyse the data using only the observations for the Canon cameras. Discuss the appropriateness of using simple linear regression and make any recommendations regarding the prediction of overall score using just the price of the camera. TABLE 14.13 Data for 28 Point-and-Shoot Digital Cameras Observation Brand Price Megapixe Weight (oz.) Score 1 Canon 330 10 7 66 2 Canon 200 12 5 66 3 Canon 300 12 7 65 4 Canon 200 10 6 62 5 Canon 180 12 5 62 6 Canon 200 12 7 61 7 Canon 200 14 5 60 8 Canon 130 10 7 60 9 Canon 130 12 5 59 10 Canon 110 16 5 55 11 Canon 90 14 5 52 12 Canon 100 10 6 51 13 Canon 90 12 7 46 14 Nikon 270 16 5 65 15 Nikon 300 16 7 63 16 Nikon 200 14 6 61 17 Nikon 400 14 7 59 18 Nikon 120 14 5 57 19 Nikon 170 16 6 56 20 Nikon 150 12 5 56 21 Nikon 230 14 6 55 22 Nikon 180 12 6 53 23 Nikon 130 12 6 53 24 Nikon 80 12 7 52 25 Nikon 80 14 7 50 26 Nikon 100 12 4 46 27 Nikon 110 12 5 45 28 Nikon 130 14 4 42
Inverse Normal Distribution
The method used for finding the corresponding z-critical value in a normal distribution using the known probability is said to be an inverse normal distribution. The inverse normal distribution is a continuous probability distribution with a family of two parameters.
Mean, Median, Mode
It is a descriptive summary of a data set. It can be defined by using some of the measures. The central tendencies do not provide information regarding individual data from the dataset. However, they give a summary of the data set. The central tendency or measure of central tendency is a central or typical value for a probability distribution.
Z-Scores
A z-score is a unit of measurement used in statistics to describe the position of a raw score in terms of its distance from the mean, measured with reference to standard deviation from the mean. Z-scores are useful in statistics because they allow comparison between two scores that belong to different normal distributions.
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Consumer Reports tested 166 different point-and-shoot digital cameras. Based upon factors such as the number of megapixels, weight (oz.), image quality, and ease of use, they developed an overall score for each camera tested. The overall score
1. Develop numerical summaries of the data.
2. Using overall score as the dependent variable, develop three
3. Using simple linear regression, develop an estimated regression equation that could be used to predict the overall score given the price of the camera. For this estimated regression equation, perform an analysis of the residuals and discuss your findings and conclusions.
4. Analyse the data using only the observations for the Canon cameras. Discuss the appropriateness of using simple linear regression and make any recommendations regarding the prediction of overall score using just the price of the camera.
TABLE 14.13 Data for 28 Point-and-Shoot Digital Cameras
Observation Brand Price Megapixe Weight (oz.) Score
1 Canon 330 10 7 66
2 Canon 200 12 5 66
3 Canon 300 12 7 65
4 Canon 200 10 6 62
5 Canon 180 12 5 62
6 Canon 200 12 7 61
7 Canon 200 14 5 60
8 Canon 130 10 7 60
9 Canon 130 12 5 59
10 Canon 110 16 5 55
11 Canon 90 14 5 52
12 Canon 100 10 6 51
13 Canon 90 12 7 46
14 Nikon 270 16 5 65
15 Nikon 300 16 7 63
16 Nikon 200 14 6 61
17 Nikon 400 14 7 59
18 Nikon 120 14 5 57
19 Nikon 170 16 6 56
20 Nikon 150 12 5 56
21 Nikon 230 14 6 55
22 Nikon 180 12 6 53
23 Nikon 130 12 6 53
24 Nikon 80 12 7 52
25 Nikon 80 14 7 50
26 Nikon 100 12 4 46
27 Nikon 110 12 5 45
28 Nikon 130 14 4 42
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