Grinfield Service company's marketing director is interested in analyzing the relationship between her company's sales and the advertising dollars spent. In the course of her analysis, she selected a random sample of 20 weeks and recorded the sales for each week and the amount spent on advertising. These data are shown below:
Weekly Sales Advertising
$2,050 $180
$3,760 $243
$1,897 $204
$2,567 $199
$4,330 $356
$5,670 $605
$2,356 $200
$3,456 $304
$1,254 $105
$4,300 $379
$3,250 $300
$4,680 $402
$4,200 $399
$2,400 $209
$1,890 $245
$3,600 $190
$5,700 $480
$5,690 $515
$2,300 $300
$1,700 $145
a) Identify the independent and dependent variables.
b) Draw a scatter plot with the dependent variable on the vertical axis and the independent variable on the horizontal axis.
c)The marketing director wishes to know if increasing the amount spent advertising increases sales. As a first attempt, use a statistical test that will provide the required information. Use a significance level of 0.025. Upon careful consideration, the marketing manager realizes that it takes a certain amount of time for the effect of advertising to register in terms of increased sales. She therefore, asks you to calculate a correlation coefficient for sales of the current week against amount of advertising spent in the previous week and conduct a hypothesis test to determine if, under this model, increasing the amount spent on advertising increases sales. Again, use a significance of 0.025.
Develop the least square regression equation for these variables. Plot the regression line on the scatter plot.
Develop a 95% confidence interval estimate for the increase in sales resulting from increasing the advertising budget by $1. Interpret the interval.
Discuss whether it is appropriate to interpret the intercept value of this model. Under what conditions is it appropriate? Discuss.
Develop a 90% confidence interval for the mean sales amount achieved during all weeks in which advertising is $200 for the week.