Problem Description:
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 17 recent models of mobile phones and gave a score out of 100 points. Several characteristics of the phone including screen size, pixel density, battery life, weight of the phone and whether the phone had a microSD slot were included in the table.
You will use descriptive statistics, inferential statisticsand your knowledge of multiple linear regression to complete this task.
Score(Dependent Variable)and several characteristics (Independent Variables) are given in the Excel file: Thursday.xlsx.
Here is a table describing the variables in the data set:
Variable Definition
Score Review of phone in points between 0 and 100
Screen Size Screen size in inches
Pixel Density (ppi) Number of pixels per square inch in the screen
Battery Life The number of minutes that the phone lasts based on several real-world scenarios including video-use, video games and web browsing
MicroSD A dummy variable indicating that the phone has external storage capability
Weight (g) Weight of the phone in grams
Required:
A. Calculate the descriptive statistics fromthe data and display in a table. Be sure to comment on the central tendency,variabilityand shape for each variable.
B. Draw a graph that displays the distribution of review scores of the phones.
C. Create a box-and-whisker plot for the distribution of the battery life of the phones and describe the shape. Is there evidence of outliers in the data?
D. Visual clarity is cited as important factor for phones, especially after Apple released the iPhone with a retina display. What is the likelihood that a phone received at least an 80 mark if the phone had at least 500 pixels per inch?Is pixel density independent of the review score? Use a Contingency Table.
E. Estimate the 95% confidence interval for the population mean pixel density of the phones.
F. Your supervisor recently stated that battery life is no longer a major issue for phones as those in production today average at least 300 minutes. Test his claim at the 5% level of significance.
G. Run a multiple linear regression using the data and show the output from Excel.
H. Is the coefficient estimate for screen size different than zero at the 10% 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.
I. Interpret the remaining slope coefficient estimates.Comment on whether the signs are what you are expecting.
J. Interpret the value of the Adjusted R2. Is the overall model statistically significant at the 1% level of significance? Use the p-value approach.
K. Do the results suggest that the data satisfy the assumptions of a linear regression: Linearity, Normality of the Errors, and Homoscedasticity of Errors? Show using scatter diagrams, normal probability plots and/or histograms and Explain.
L. Based on the results of the regressions, is it likely that other factors have influencedthe review score? If so, provide a couple possible examples and indicate whether these would likely influence the regression results if they were included.
M. If a community housing organisation asked for information regarding the characteristics of housing targeting the households of Aboriginals and Torres Strait Islanders, explain whether a clustered sampling technique of the CBD would provide an accurate representation of these households. (Note: This question does not use the data)
Allocation of Marks:
Professional Business Report 2 Marks
Part A 1 Mark
Part B 1 Mark
Part C 1 Mark
Part D 2 Marks
Part E 1 Mark
Part F 1 Mark
Part G 1 Mark
Part H 2 Marks
Part I 2 Marks
Part J 1 Mark
Part K 3 Marks
Part L 1 Mark
Part M 1 Mark
Total: 20 Marks