Question

A local grocery store wants to predict the monthly sales in dollars. The manager believes that the amount of newspaper advertising significantly affects the store sales. The manager randomly selects 10 months of data consisting of monthly grocery store sales (in thousands of dollars) and advertising expenditures (in thousands of dollars). See the following data:

Is there a linear relationship between sales and the advertising expenditures? if yes, is it positive or negative? is this relationship strong? use the correlation coefficient to support your answer.

Develop the equation of the simple regression line to predict sales from advertising expendi- tures using the data below. Interpret each one of the parameters.

Explicitly state, in words, any assumptions this model must verify in order to perform the statistical inference.

Advertising	2.74	2.87	2.93	2.87	2.98	3.09	3.36	3.61	3.75	3.95
Sales	99.9	97.9	98.9	87.9	92.9	97.9	100.6	104.9	105.3	108.6

Answer 1

Hence there exits a positive relationship between sales and the advertising expenditures.

Hence there exists strong correlation between sales and the advertising expenditures.

The slope of a regression line (b) represents the rate of change in y as x changes, so for every increase in advertisement cost, sales changes to 11.34476

The intercept (often labeled the constant) is the expected mean value of Y when all X=0. Hence when advertisement cost is 0 sales value would be 63.0066