DSC 670 Assignment 9
x | y | ||
2 | 12 | ||
3 | 9 | ||
6 | 8 | ||
7 | 7 | ||
8 | 6 | ||
7 | 5 | ||
9 | 2 |
a. | Develop the least squares estimated regression equation. |
b. | At 95% confidence, perform a t test and determine whether or not the slope is significantly different from zero. |
c. | Perform an F test to determine whether or not the model is significant. Let a = 0.05. |
d. | Compute the coefficient of determination. |
x | y | |
2 | 12 | |
3 | 9 | |
6 | 8 | |
7 | 7 | |
8 | 6 | |
7 | 5 | |
9 | 2 |
å x = 154 | å x^{ 2} = 2,586 | å y = 451 | å y^{ 2} = 18,901 | å x y = 5,930 |
a. | Using the above information, develop the least-squares estimated regression line. |
b. | Compute the coefficient of determination. |
c. | Perform an F test and determine whether or not there is a significant relationship between demand and unit price. Let a = 0.05. |
d. | Perform a t test to determine whether the slope is significantly different from zero. Let a = 0.05. |
e. | Would the demand ever reach zero? If yes, at what price would the demand be zero? Show your complete work. |
ANOVA | |||||
df | SS | ||||
Regression | 1 | 50.58 | |||
Residual | 13 | 55.42 | |||
Total | 14 | 106.00 | |||
Coefficients | Standard Error | t Stat | |||
Intercept | 16.156 | 1.42 | |||
Variable x | -0.903 | 0.26 |
a. | Perform a t test and determine whether or not y and x are related. Use a = 0.05. |
b. | Compute the coefficient of determination and fully interpret the meaning. Be very specific. |
ANOVA | |||||
df | SS | ||||
Regression | 1 | 882 | |||
Residual | 20 | 4000 | |||
Total | 21 | 4882 | |||
Coefficients | Standard Error | t Stat | |||
Intercept | 5.00 | 3.56 | |||
Variable x | 6.30 | 3.00 |
a. | What has been the sample size for the above? |
b. | Perform a t-test and determine whether or not x and y are related. Use a = 0.05. |
c. | Perform an F-test and determine whether or not x and y are related. Use a = 0.05. |
d. | Compute the coefficient of determination. |
e. | Interpret the meaning of the value of the coefficient of determination that you found in d. Be very specific. |
x | y | ||
2 | 12 | ||
3 | 9 | ||
6 | 8 | ||
7 | 7 | ||
8 | 6 | ||
7 | 5 | ||
9 | 2 |
a. | What is the estimated regression equation? | |
b. | Perform a t test and determine whether or not x and y are related. Use a = 0.05. | |
c. | Perform an F test and determine whether or not x and y are related. Use a = 0.05. | |
d. | Find and interpret the coefficient of determination. | |
Week | Price | Sales | ||
1 | .33 | 20 | ||
2 | .25 | 14 | ||
3 | .44 | 22 | ||
4 | .40 | 21 | ||
5 | .35 | 16 | ||
6 | .39 | 19 | ||
7 | .29 | 15 |
a. | What is the estimated regression equation? |
b. | Perform a t test and determine whether or not x and y are related. Use a = 0.05. |
c. | Perform an F test and determine whether or not x and y are related. Use a = 0.05. |
d. | Find and interpret the coefficient of determination. |
Month | Sales | Month | Sales | Month | Sales |
1 | 12.8 | 7 | 20.6 | 12 | 23.8 |
2 | 14.6 | 8 | 18.5 | 13 | 25.1 |
3 | 15.2 | 9 | 19.9 | 14 | 24.7 |
4 | 16.1 | 10 | 23.6 | 15 | 26.5 |
5 | 15.8 | 11 | 24.2 | 16 | 28.9 |
6 | 17.2 |
Using simple linear regression, forecast the number of subscribers for months 17, 18, 19, and 20.
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