Question

*For full credit, your interpretations must be full sentences and must describe them quantitatively.

Do the following: Please answer the following.

- Create a scatterplot and comment on the relationship between website hits and weekly revenue

- Compute correlation and test for significance

– provide both the correlation and the p-value

- Conduct linear regression using Excel

- What is the regression equation?

- What are weekly revenues if there are no website hits? Is this value significant at an alpha=0.05 level?

- How much do weekly revenues increase for every additional website hit? Is this significant at an alpha=0.05 level?

How high could this amount be? How low could this amount be?

- How much variation in revenue can be explained by website hits?

- Create a normal probability plot. Comment on the assumption of normally distributed errors.

- Create a plot of residuals. Comment on whether or not the residuals are random or exhibit a pattern.

12.15 Below are fitted regressions for Yasking price of a used vehicle and X-the age of the vehicle. The observed range of X was 1 to 8 years. The sample consisted of all vehicles listed for sale in a particular week. (a) Interpret the slope of each fitted regression. (b) Interpret the intercept of each fitted regression. Does the intercept have meaning? (c) Predict the price of a 5-year-old Chevy Blazer. (d) Predict the price of a 5-year-old Chevy Silverado.CarPrices Chevy Blazer: Price-16,189 1,050 Age (n -21 vehicles, observed X range was 1 to 8 years) Chevy Silverado: Price 22,591 - 1,339 Age (n -24 vehicles, observed X range was 1 to 10 years). DATA SETF Restaurant Weekly Revenue and Weekly Website Hits (n 10 restaurants)WebSiteHits Website Hits Weekly Revenue Restaurant 1,213 1,490 1,365 1,455 1,269 1,632 1,323 1,865 1,590 1,878 $12,113 11,409 14,579 11,605 12,308 12,320 13,225 13,652 13,893 13,896 John's Café Buccan New City Diner Black Pearl Saratoga Burnt Toast University Seat Jimmy's Maroon and Orange Burger Palace

Answer 1

A)

16000 14000 12000 10000 8000 6000 2000 200 400 600 800 1000 1200 1400 1600 1800 2000

B)

x	y
1213	12113
1490	11409
1365	14579
1455	11605
1269	12308
1632	12320
1632	13225
1865	13652
1590	13893
1878	13896
r	0.413288

formula

x	y
1213	12113
1490	11409
1365	14579
1455	11605
1269	12308
1632	12320
1632	13225
1865	13652
1590	13893
1878	13896
r	=CORREL(A2:A11,B2:B11)

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.4133
R Square	0.1708
Adjusted R Square	0.0672
Standard Error	1051.8602
Observations	10
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1823294.5796	1823294.5796	1.6479	0.2352
Residual	8	8851279.4204	1106409.9275
Total	9	10674574.0000
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	9836.2199	2409.7093	4.0819	0.0035	4279.4202
x	1.9909	1.5509	1.2837	0.2352	-1.5854

regression equation is

y^= 9836.2199 + 1.9909 x

p-value = 0.2352

p-value > alpha

hence we fail to reject the null hypothesis

What are weekly revenues if there are no website hits? Is this value significant at an alpha=0.05 level?

when x = 0

y^= 9836.2199

p-value for intercept = 0.0035

p-value < alpha

hence this value is significant

- How much do weekly revenues increase for every additional website hit? Is this significant at an alpha=0.05 level?

slope =1.9909

hence weekly revenues increase by 2 for every additional website hit

this value is not significant

How much variation in revenue can be explained by website hits

this is given by R^2 = 0.1708

hence 17.08 %