Worldwide sales of mobile phones are a multi-billion dollar business. There is s
ID: 3066540 • Letter: W
Question
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.
You will use descriptive statistics, inferential statistics and your knowledge of multiple linear regressionto complete this task.
Score (Dependent Variable) and several characteristics (Independent Variables) are given in the Excel file: Assignmentdata.xlsx.
Here is a table describing the variables in the data set:
Variable
Definition
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
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.
(1 Mark)
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 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)
Is the overall model statistically significant at the 5% level of significance? Use the p-value approach.
(1/2 Mark)
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)
Data:
Variable
Definition
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
Explanation / Answer
> data1=read.csv(file.choose(),header=T)
> data1
Phone Score Pixle.Density..PPI. Battery.Score Fingerprint
1 Samsung Galaxy S9+ 91 529 70 1
2 Samsung Galaxy S9 90 568 60 1
3 iPhone X 90 463 54 0
4 HTC U11 87 402 79 1
5 LG Aristo 2 72 294 48 0
6 LG X4+ 79 277 60 1
7 Motorola Moto E5 80 294 60 1
8 Motorola Moto X5 85 373 66 1
9 Nokia 6 (2018) 89 401 60 1
10 Sony Xpreia 92 424 64 1
11 Sony Xperia XA2 86 424 66 1
12 iPhone 8 Plus 87 401 54 1
13 Google Pixel 2 90 441 54 1
14 Microsoft Lumia 650 82 294 40 0
15 Vodafone Smart V8 83 401 60 1
16 Vodafone Smart E8 74 196 44 0
17 Blackberry Motion 85 401 80 1
18 Blackberry Aurora 82 267 60 0
19 Hisense Elegance 1 (E76) 80 401 60 1
20 Hisense U962 70 196 40 0
21 Hisense T5 Plus 70 267 44 0
22 iPhone 7 91 326 39 1
23 LG G6 93 439 60 1
24 Sony Xperia XA2 Ultra 86 367 72 1
25 Telstra Signature 2 75 277 56 1
26 Telstra Tough Max2 75 294 60 1
27 Panasonic P100 71 294 44 1
28 Sharp R1S FS8028 79 267 100 1
29 Huawei Enjoy 8 79 269 58 1
Android Windows iOS
1 1 0 0
2 1 0 0
3 0 0 1
4 1 0 0
5 1 0 0
6 1 0 0
7 1 0 0
8 1 0 0
9 1 0 0
10 1 0 0
11 1 0 0
12 0 0 1
13 1 0 0
14 0 1 0
15 1 0 0
16 1 0 0
17 1 0 0
18 1 0 0
19 1 0 0
20 1 0 0
21 1 0 0
22 0 0 1
23 1 0 0
24 1 0 0
25 1 0 0
26 1 0 0
27 1 0 0
28 1 0 0
29 1 0 0
> names(data1)
[1] "Phone" "Score" "Pixle.Density..PPI."
[4] "Battery.Score" "Fingerprint" "Android"
[7] "Windows" "iOS"
a)
> summary(data1)
Phone Score Pixle.Density..PPI.
Blackberry Aurora : 1 Min. :70.00 Min. :196.0
Blackberry Motion : 1 1st Qu.:79.00 1st Qu.:277.0
Google Pixel 2 : 1 Median :83.00 Median :367.0
Hisense Elegance 1 (E76): 1 Mean :82.52 Mean :353.3
Hisense T5 Plus : 1 3rd Qu.:89.00 3rd Qu.:402.0
Hisense U962 : 1 Max. :93.00 Max. :568.0
(Other) :23
Battery.Score Fingerprint Android Windows
Min. : 39.00 Min. :0.0000 Min. :0.0000 Min. :0.00000
1st Qu.: 54.00 1st Qu.:1.0000 1st Qu.:1.0000 1st Qu.:0.00000
Median : 60.00 Median :1.0000 Median :1.0000 Median :0.00000
Mean : 59.03 Mean :0.7586 Mean :0.8621 Mean :0.03448
3rd Qu.: 64.00 3rd Qu.:1.0000 3rd Qu.:1.0000 3rd Qu.:0.00000
Max. :100.00 Max. :1.0000 Max. :1.0000 Max. :1.00000
iOS
Min. :0.0000
1st Qu.:0.0000
Median :0.0000
Mean :0.1034
3rd Qu.:0.0000
Max. :1.0000
> attach(data1)
b)
> boxplot(Score)
c)
> boxplot(Battery.Score)
d)
> denominator=length(which(Battery.Score>70))
> denominator
[1] 4
> numerator=length(which(Score>70&Battery.Score>70))
> numerator
[1] 4
Probability = 4/4 = 1
Phone rating is independent of battery score.
e)
> t.test(Score,conf.level=0.9)
One Sample t-test
data: Score
t = 62.328, df = 28, p-value < 2.2e-16
alternative hypothesis: true mean is not equal to 0
90 percent confidence interval:
80.26508 84.76940
sample estimates:
mean of x
82.51724
f)
> Android=as.factor(Android)
> Fingerprint=as.factor(Fingerprint)
> Windows=as.factor(Fingerprint)
> model=lm(Score~Battery.Score+Android+Fingerprint+Windows+Pixle.Density..PPI.)
> summary(model)
Call:
lm(formula = Score ~ Battery.Score + Android + Fingerprint +
Windows + Pixle.Density..PPI.)
Residuals:
Min 1Q Median 3Q Max
-6.6866 -2.8657 -0.1154 2.0230 6.4086
Coefficients: (1 not defined because of singularities)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 62.958563 4.230129 14.883 1.29e-13 ***
Battery.Score 0.088765 0.068954 1.287 0.21026
Android1 -6.609877 2.349542 -2.813 0.00963 **
Fingerprint1 2.108157 2.125514 0.992 0.33117
Windows1 NA NA NA NA
Pixle.Density..PPI. 0.052123 0.009291 5.610 8.95e-06 ***
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1
Residual standard error: 3.897 on 24 degrees of freedom
Multiple R-squared: 0.7439, Adjusted R-squared: 0.7012
F-statistic: 17.43 on 4 and 24 DF, p-value: 7.908e-07
Battery score is statistically insiginificant since p-value > 0.05.
Adjusted R square = 0.7012 implies that 70.12% of the total variation is explained by the fitted regression model.
There is a difference between R square and adjusted R-square since adjusted R square takes into consideration the number of observations and predictor variables used for the model.
The overall model is statistically significant since p-value is very small.
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