Worldwide sales of mobile phones are a multi-billion dollar business. There is severe competition among the major manufacturers to attract higher sales and greater market shares. To achieve this, companies compete with each other on prices. However, for many customers, price may not be as important as the perceived quality of the phone, especially as many phones are offered at “zero price” under various plans and contracts from service providers.
Decision makers and markets at mobile-phone manufacturers would like to know what features of a mobile phone are important to consumers. This would be especially important in helping to design effective marketing and advertising campaigns. A review site reviewed 29 recent models of mobile phones and gave a score out of 100 points. Several characteristics of the phone including pixel density, battery life, whether the phone had a fingerprint scanner along with the operating system were included in the table.
Score-Review of phone in points between 0 and 100
Pixel Density (ppi)-Number of pixels per square inch in the screen
Battery Scores-The number of hours that the phone lasts based on several real-world scenarios including video-use, web browsing and phone calls.
Fingerprint-A dummy variable to indicate if the phone has a fingerprint scanner
Android-Dummy variable to indicate that the phone uses a version of Android
Windows-Dummy variable to indicate that the phone uses a mobile version of Windows
iOS-Dummy variable to indicate that the phone uses iOS
A. Calculate the descriptive statistics from the data and display in a table. Be sure to comment on the central tendency, variability and shape for Score, Pixel Density and Battery Score. How would you interpret the mean of dummy variables such as Fingerprint or Android? (1 Mark)
B. Draw a graph that displays the distribution of review scores. Be sure to comment on the distribution.
C. draw box-and-whisker plot for the distribution of Battery Scores and describe the shape. Is there evidence of outliers in the data? (1 Mark)
D. What is the likelihood that a phone will receive a rating higher than a 70 if the battery score measure is greater than a 70? Is the phone rating statistically independent of the battery score? Use a Contingency Table. (2 Marks)
E. Estimate the 90% confidence interval for the population mean review score of phones. (1 Mark)
F. Your supervisor recently stated that older mobiles typically had a battery score of around 50, but have recently been improving. Test his claim at the 5% level of significance. (1 Mark)
G. Run a multiple linear regression using the data and show the output from Excel. Note: exclude the dummy variable “iOS” when running the multiple regression. Also, remember to tick all the graph options which may help you answer Part N. (1 Mark)
H. Is the coefficient estimate for the Battery Score statistically different than zero at the 5% level of significance? Set-up the correct hypothesis test using the results found in the table in Part (G) using both the critical value and p-value approach. Interpret the coefficient estimate of the slope. (2 Marks)
I. Interpret the remaining slope coefficient estimates. Discuss whether the signs are what you are expecting and explain your reasoning. (2 Marks)
J. Interpret the value of the Adjusted R2. Is there a large difference between the R2 and the Adjusted R2? If so, what may explain the reasoning for this? (1/2 Mark)
K. Is the overall model statistically significant at the 5% level of significance? Use the p-value approach.
L. Based on the results of the regressions, what other factors would have influenced the review score? Provide a couple possible examples and indicate their predicted relationship with the review score if they were included. (1 Mark)
M. Predict the average review score of a phone with a pixel density of 400 ppi, a battery score of 90 that has a fingerprint scanner and uses Windows if it is appropriate to do so. Show the predicted regression equation. (1 Mark)
N. Do the results suggest that the data satisfy the assumptions of a linear regression (that is, Linearity, Normality of the Errors, and Homoscedasticity of Errors)? Show using residual plots, normal probability plots and/or histograms and Explain. (2 Marks)
Would these results tell us anything about the average satisfaction that users have with the features of their phones? If not, describe a scenario in how you would construct a sample that reflects users’ satisfaction