15 Feb Linear Correlation and Regression Worksheet Laura has just started her first job as a marketing analyst at a toy store. Her first assignment is to study the advertising expenses an
Linear Correlation and Regression Worksheet
Laura has just started her first job as a marketing analyst at a toy store. Her first assignment is to study the advertising expenses and toys sales of the company during the past 12 months. She wants to know if there is any relationship between advertising expenditure and sales. With the information, she would like make recommendation to her supervisor of an appropriate advertising expense to increase sales of the company.
Here is the advertising and sales information Laura obtained from the company database.
Advertising Expenditure Monthly Sales
$ 12,500 $ 330,250
$ 20,000 $ 400,500
$ 13,500 $ 352,500
$ 22,000 $ 412,500
$ 15,700 $ 368,000
$ 19,800 $ 395,000
$ 10,000 $ 295,000
$ 23,500 $ 425,000
A scatter plot that captures the data given. Remember to give an appropriate title and label the axes clearly.
Find the linear correlation. Do the variables have a positive or negative association? Is the linear association between the two variables strong or weak?
Can we say that the advertising expenditure causes the sales to go up or down?
Sketch an approximation of the least squares regression line on the chart in part 1. Then use a calculator or computer program to find the algebraic form of the regression line.
What is the slope of the regression equation? What does it mean?
What is the y-intercept of the regression equation? What does it mean?
Use the regression equation, find the estimated sales if the company spends $22,500 on advertising.
If the sales this month is $350,000, what would Laura expect the company spent on advertising?
Laura is very excited to see that if there appears to have a relationship between advertising expense and sales. Use the regression equation to find the estimated sales if the company spends $40,000 on advertising. Is it reasonable?
Laura brings the figure she found in problem 9 to her supervisor and suggests the company to spend $40,000 in advertising the following month.
One month later, Laura was surprised to find out that the sales did not reach the expected amount. The sales improved, but it was only $480,000. Can you explain why it happened?
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