Question 1. The manager of a chain of six movie rental shops randomly sampled dail y sales and other data  from each of the shops to investigate sales patterns and the effectiveness of promotions. The following variables were recorded:  

income.total     the total income for the shop on the day 

income.rental    the income from movie rentals on the day 

income.games    the income from computer game rentals on the day 

income.sales     the income from sales (of drinks, confectionaries, etc) on the day 

new.releases      the number of new titles released in the prior week 

customers          the number of customers who visited the shop on the sampled day 

shop                which of the shops was sampled (coded as “A”, “B”, …, “F”) 

day                   the day the shop was sampled (coded as “Mon”, “Tue”, …, “Sun”) 

date                   the date the shop was sampled 

tv.ads                were television advertisements for the  shops being played in the week prior to the sampled day (coded as                          “Yes” or “No”) 

promotion         the type of promotion offer available on the sampled day (coded as “Vouchers”, “Discount” or “None”) 

weather            the weather conditions at the shop on the sampled day (coded as “Fine”, “Overcast”, “Light.Rain” or                                            “Heavy.Rain”)

Notes on Question 2 - 4: 

• For these questions we want you to do the full analysis and write a Report. Your answers should be in three parts.  First: Technical Notes on the analysis. See the Case Studies.  Second: Executive Summary of the main findings of the analysis. See the Case Studies.  Third: R output. Include all necessary R output used in answering all of these questions as an appendix at the end of your assignment. These are for the markers to refer to if you make any mistakes in your analysis, so they can consider giving partial credit. There are no marks allocated for the R output, all the marks are for the Technical Notes and Executive Summary. 

Please try to keep this section as small as possible – use the layout20x() command to save space for multiple plots.Remember: When you cut and paste R output into a word processor, you should use a “fixed” font such as Courier. 

Question 2.  An inspector at the US National Transportation Safety Board was interested in whether the level of head injuries sustained in car crashes differs depending on the size of the vehicle driven. Standard automobiles containing crash-test dummies are driven into a wall at 55 kph. 

The resulting data is stored in the text file "crash" which contains the variables:  Head the level of head injury assessed by measuring the damage to the head of the crash-test dummy  Size the size of the vehicle tested: Light, Medium, Heavy or Van 

Question 3.Researchers were interested in how long different types of outdoor paint lasted before beginning to crack, flake and peel in different climates. Random samples of two types of outdoor paint, enamel and latex, were tested in four geographic locations in the United States. The resulting data are stored in the text file "paint" which contains the variables:  

Lasted              the amount of time before the paint began to crack, flake and peel (in months) 

Location            the location in the United States: 

                       North, West, South  or East 

Paint                the type of paint: 

                       Enamel   or Latex 

Several scenarios for analysing the data are given below. 

Scenario 1:  Is there any relationship between the weather conditions and the day? 

Scenario 2:  Do the weather conditions and the day of the week affect the total daily income? 

Scenario 3:  Does the total daily income differ between the shops? 

Scenario 4:  Is the daily income from movie rentals able to be predicted by the number of customers who visited the shop on the sampled day? 

Scenario 5:  Does the total daily income differ depending on whether or not television advertisements for the shops were played in the previous week?

For each of the five scenarios: 

(i) Identify ALL variables of interest. Classify each of them as either qualitative or quantitative.  

(ii) Is there a response variable, or are we interested in analysing counts? If there is a response variable, what is it?  

(iii) State which of the following types of analysis would be most appropriate:

A: One-way Table of Counts 

B: Two-way Table of Counts 

C: One sample t-test 

D: Paired data t-test 

E: Two-sample t-test 

F: Regression 

G: One-way ANOVA 

H: Two-way ANOVA