*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.
A)
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 %
*For full credit, your interpretations must be full sentences and must describe them quantitatively. Do the following: P...