numBrands sales 15 651.06 30 728.92 19 725.34 25 735.48 21 737.04 19 706.22 17 663.94 21 741.6 21 739.95 15 636.44 15 651.58 16 638.45 26 761.92 25 759.08 13 573.34 13 588.97 23 734.74 26 758.79 20 701.94 12 557.84 18 687.5 27 769.38 17 678.67 13 568.66 23 770.24 15 608.31 22 744.26 18 695.06 22 747.36 33 715.59 Sara is local grocery store owner that recently found out that her manager, Joe, in charge of placing new orders of cookies has been very lazy this year. Some weeks, Joe would have forgotten to place an order to replace the brands of cookies the store ran out of. When Joe forgot to order more cookies, he just filled the shelves with more boxes of the brands that he had left. As a result, the number of brands of cookies that customers could buy changed a fair amount form week to week. While upset that she had to replace Joe, Sara decided to try to get some use out of this bad situation. Sara realized that she can use the sales numbers from this time period to study the relationship between the weekly sales of cookies and the number of brands that were available that week. In the data file ``Cookie.Sales'' Sara has collected the sales and brand availability for the past thirty weeks. The ``numBrands'' variable indicates how many brands of cookies were available in each week and the ``sales'' variable indicates the total sales, in dollars, of cookies in each week. Hypothesize the simple linear regression model that Sara should use. Be sure to include all assumptions being made. Check the model assumptions. Obtain the slope and intercept estimates of your simple linear regression in R. Interpret the slope in terms of the relationship between the number of brands of cookies and the weekly sales of cookies.
numBrands sales
15 651.06
30 728.92
19 725.34
25 735.48
21 737.04
19 706.22
17 663.94
21 741.6
21 739.95
15 636.44
15 651.58
16 638.45
26 761.92
25 759.08
13 573.34
13 588.97
23 734.74
26 758.79
20 701.94
12 557.84
18 687.5
27 769.38
17 678.67
13 568.66
23 770.24
15 608.31
22 744.26
18 695.06
22 747.36
33 715.59
Sara is local grocery store owner that recently found out that her manager, Joe, in charge of
placing new orders of cookies has been very lazy this year. Some weeks, Joe would have forgotten to place an order to replace the brands of cookies the store ran out of. When Joe forgot to order more cookies, he just filled the shelves with more boxes of the brands that he had left. As a result, the number of brands of cookies that customers could buy changed a fair amount form week to week.
While upset that she had to replace Joe, Sara decided to try to get some use out of this bad situation.
Sara realized that she can use the sales numbers from this time period to study the relationship between the weekly sales of cookies and the number of brands that were available that week.
In the data file ``Cookie.Sales'' Sara has collected the sales and brand availability for the past thirty weeks. The ``numBrands'' variable indicates how many brands of cookies were available in each week and the ``sales'' variable indicates the total sales, in dollars, of cookies in each week.
- Hypothesize the simple linear regression model that Sara should use. Be sure to include all assumptions being made.
- Check the model assumptions.
- Obtain the slope and intercept estimates of your simple linear regression in R. Interpret the slope in terms of the relationship between the number of brands of cookies and the weekly sales of cookies.
- Would it be appropriate to interpret the intercept as the average weekly sales of cookies when no brands of cookies are available? Why or why not?
- How useful does the model appear to be? Be clear about what metrics you are using and interpret these (coeff of determination, model standard error).
- Conduct a test for the slope and interpret the p-value. Is the slope found to be statistically significant at the 5% significance level?
- Construct a 90% confidence interval for the true average weekly sales when the store has 30 brands of cookies available. Interpret the interval in context.
- Construct a 90% prediction interval for a new week's sales when the store has 30 brands of cookies available that week. Interpret the interval in context.
Trending now
This is a popular solution!
Learn your way
Includes step-by-step video
Step by step
Solved in 4 steps with 6 images
