Mathematics

**Required:**

- 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)** - Draw a graph that displays the distribution of review scores. Be sure to comment on the distribution.
- Create a box-and-whisker plot for the distribution of Battery Scores and describe the shape. Is there evidence of outliers in the data?
**(1 Mark)** - 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)** - Estimate the 90% confidence interval for the population mean review score of phones.
**(1 Mark)** - 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)** - 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)** - 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)** - Interpret the remaining slope coefficient estimates. Discuss whether the signs are what you are expecting and explain your reasoning.
**(2 Marks)** - Interpret the value of the Adjusted R
^{2}. Is there a large difference between the R^{2}and the Adjusted R^{2}? If so, what may explain the reasoning for this?**(1/2 Mark)** - Is the overall model statistically significant at the 5% level of significance? Use the p-value approach.
- 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)** - 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)** - 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.

**(1 Mark)**

**(1/2 Mark)**

**(1 Mark)**

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