Question

#2. The operations manager of a musical instrument distributor feels that demand for a particular type of guitar may be related to the number of YouTube views for a popular music video by the popular rock group Marble Pumpkins during the preceding month. The manager has collected the data shown in the following table: YouTube Views (1000s) Guitar Sales 30 8 40 11 70 12 60 10 80 15 50 13

a. Graph the data to see whether a linear equation might describe the relationship between the views on YouTube and guitar sales.

b. Using the equations presented in this chapter, compute the SST, SSE, and SSR. Find the least squares regression line for the data.

c. Using the regression equation, predict guitar sales if there were 40,000 views last month.

Answer 1

a. Graph the data to see whether a linear equation might describe the relationship between the views on YouTube and guitar sales.

The graph for the data using Excel is:

b. Using the equations presented in this chapter, compute the SST, SSE, and SSR. Find the least squares regression line for the data.

The output for the problem using Excel is:

	r²	0.593	n	6
	r	0.770	k	1
	Std. Error	1.732	Dep. Var.	Guitar Sales
ANOVA table
Source	SS	df	MS	F	p-value
Regression	17.5000	1	17.5000	5.83	.0731
Residual	12.0000	4	3.0000
Total	29.5000	5
Regression output					confidence interval
variables	coefficients	std. error	t (df=4)	p-value	95% lower	95% upper
Intercept	6.0000
Youtube Views (1,000s)	0.1000	0.0414	2.415	.0731	-0.0150	0.2150

SST = 29.5

SSE = 12

SSR = 17.5

The least squares regression line for the data is:

Guitar Sales = 6 + 0.1Youtube Views (1,000s)

c. Using the regression equation, predict guitar sales if there were 40,000 views last month.

The output for the problem using Excel is:

Predicted values for: Guitar Sales
		95% Confidence Interval		95% Prediction Interval
Youtube Views (1,000s)	Predicted	lower	upper	lower	upper	Leverage
40	10.000	7.387	12.613	4.527	15.473	0.295

The predicted guitar sales if there were 40,000 views last month is 10.