a.

In seeking to determine how influential advertising is, the management of a recently established retail chain collected data on sales revenue and advertising expenditure from its' stores over the last ten (10) weeks. The table below shows the data collected:

Advertising Expenditure ($ 000) 3 5 7 6 3.5 4 4.5 7 7.5 8.5

Sales ($ 000) 50 250 700 450 75 150 200 750 800 1,100

1. If they are going to run a linear regression, identify which variable should be the independent variable and which should be the dependent variable in a regression equation.

2. Estimate the slope and intercept coefficients of the linear regression model.

3. If advertising expenditure is equal to $9,000, estimate the total sales income.

b.

A retail shop manager analyzed the relationship between sales and the method of payments. Based on his analysis, he has produced the following joint probability table, as shown below:

Size of purchase Method of payment

Cash Credit card Debit Card

Under $20 0.09 0.03 0.04

$20 -$100 0.05 0.21 0.18

Over $100 0.03 0.23 0.14

1. What proportion of purchases were paid by debit card?

2. What proportion of purchases were paid by cash?

3. Determine the proportion of purchases made by credit card or by debit card?

4. Are the events "payment by cash" and "purchase of under $20" mutually exclusive? Explain your answer.