Analysis And Statistics | Proportion Of The Variation In Sales

onsider the following regression model between the dependent variable, SALES (reflecting monthly sales, in thousands of dollars) and independent variable, ADVERTISING (representing the monthly advertising expenditure, in thousands of dollars):
Estimated SALES = 4.2 + 2.6 ADVERTISING.
The value 4.2 in the above regression line represents:
Select one:

a. the proportion of the variation in SALES explained by variation in ADVERTISING

b. the change in SALES, on average, following a unit increase in ADVERTISING

c. a ratio of SALES over ADVERTISING as a percentage

d. the estimated value of SALES when ADVERTISING is zero

Q1
Consider the following regression model between the dependent variable, SALES (reflecting monthly sales, in thousands of dollars) and independent variable, ADVERTISING (representing the monthly advertising expenditure, in thousands of dollars):
Estimated SALES = 4.2 + 2.6 ADVERTISING.
The value 4.2 in the above regression line represents:
Select one:
a. the proportion of the variation in SALES explained by variation in ADVERTISING
b. the change in SALES, on average, following a unit increase in ADVERTISING
c. a ratio of SALES over ADVERTISING as a percentage
d. the estimated value of SALES when ADVERTISING is zero
Q2.
A company is considering an organisational change by instituting a policy whereby an employee could take one additional day off per month without pay. To assess the attitudes of company employees towards this change, a sample of 400 employees is selected and asked whether they favour the institution of time off without pay in the organisation. Three responses were permitted: favour, neutral or oppose. The results of the survey, cross-classified by type of job and attitude towards time off without pay, are summarised in the contingency table below.
Type of job Attitude towards time off without pay
Favour Neutral Oppose
Hourly worker 135 23 67
Supervisor 39 7 14
Middle management 47 6 22
Upper management 26 6 8
At the 1% significance level, is there evidence of an association between attitude towards time off without pay and type of job?
You will need to enter the data (given in the contingency table above) into Excel to answer the questions below.
The chi-square test statistic and the p-value must be reported to 4 d.p.
The answer to the last question must be written as either: not rejected or rejected.
The chi-square test statistic is Answer .

The associated p-value is Answer .

This means that H0, that there is no association between attitude towards time off without pay and type of job, should be Answer .
Q3
A social scientist wishes to analyse the relationship between crime rates and the youth unemployment rate. He collects data on the number of break and enters per 1,000 people and youth unemployment rate measured over a 17 months period. The results are shown in the table below.
Unemployment
25 21
23 20
22 18
19 17
20 22
15 17
18 16
14 22
23 25
26 27
16 16
14 18
13 16
12 13
13 19
17 15
27 30
Copy the data into Excel and carry out a regression analysis. Give all your answers to 2 decimal places.
The regression equation is
estimated crime rate = Answer + Answer unemployment rate
The coefficient of determination is = Answer
Q4.
The Australian Tertiary Admission Rank (ATAR) is the main criterion used for entry into most undergraduate programs at universities in Australia. A management lecturer wishes to investigate whether a student’s ATAR influences their subsequent performance in a first-year Principles of Management subject. He collected data on a student’s ATAR and their management mark, and carried out a Regression analysis using Excel.
Some of the Excel output is reproduced below. Test if there is a linear relationship between a student’s ATAR and their management mark. Use a 1% test.