David Ding advertises on a local radio station. For the past six week, the manag

Question

David Ding advertises on a local radio station. For the past six week, the manager has kept records of the humber of minutes of advertising that were purchased, and the sales for that week. Week 1, 2 minutes of advertising with $1,400 in sales. Week 2, 1 minute, $920 in sales. Week 3, 3 minutes advertising, $1,100 in sales. Week 4, 5 minutes of advertising with $2,265 in sales. Week 5, 5 minutes of advertising, $2,8990 in sales. Week 6, 4 minutes in advertising, $2,200 in sales.
1. What is the y-intercept, the slope and the correlation coefficient from the above data 2. Estimate sales if 7 minutes of advertising were purchases. 3. Estimate sales if 8 minutes were purchases. 4. How many minutes of advertising should David buy to attain sales of $3,000?

Explanation / Answer

Here are the directions on how to do this:
http://en.wikipedia.org/wiki/Simple_linear_regression#Fitting_the_regression_line

Here are the answers:

y = 374 + 427x, R^2 = 0.808093 (R^2 is the coefficient of determination), R = Sqrt(R^2) = 0.89894 (R is the correlation coefficient)

Using this equation, we plug in 7 and 8 min for x to obtain the two estimates of:
$3363 for 7 min of advertising
$3790 for 8 min of advertising

We then plug in 3000 in for y and solve for x to obtain the required minutes of advertising to obtain sales of $3,000.
The answer we get is x = 6.14988 min

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