Homework SourseShown below is a portion of a computer output for a regressi
Shown below is a portion of a computer output for a regression analysis relating y (dependent variable) and x (independent variable).
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 alpha .05. The critical value is |2.11|.
B. Compute the coefficient of determination and fully interpret the meaning. Be very specific.
Shown below is a portion of a computer output for a regression analysis relating y (dependent variable) and x (independent variable).
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 alpha .05. The critical value is |2.11|.
B. Compute the coefficient of determination and fully interpret the meaning. Be very specific.
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 alpha .05. The critical value is |2.11|.
B. Compute the coefficient of determination and fully interpret the meaning. Be very specific.
Solution
ANOVA
df SS MSS F
Regression 1 50.58 50.58 11.8646
Residual 13 55.42 4.2631
Total 14 106.00 . Here the calculated value of F is greater than tabulated value, so Y and X are not related. The coefficient of determination means the percent of the data that it is closest to the line of best fit. r(Y/X)=-.903(.26/1.42)=-.1653, r2=.02732, 2% of the total variation inY can be explained by the linear relationship between X and Y.
