Question

1. each Given the following data comes from the football program of a quaint university north of here that wears blue and yellow. Evaluate this data for linear regression:

penalties	points scored
3	49
5	38
7	21
6	24
9	17
6	28

1. Make a scatter plot
2. Which variable is the predictor or explanatory variable and which is the response variable?
3. Conduct a hypothesis test to determine if there is a significant linear correlation
   1. State your null and alternative hypothesis
   2. Justify rejecting or failing to reject the null at the .05 significance level.
4. Provide the equation
5. Determine r
6. What percent of the variation in points scored is accounted for by the regression equation?
7. Find the residual of 7 penalties.
8. Estimate the number of points scored if Quaint U is penalized 6 times in the game
9. Estimate the number of points scored if Quaint U is penalized 80 times in the game
10. Determine the 95% confidence interval for the slope coefficient
11. Sketch a plot of the standardized residuals on the vertical axis against y on the horizontal. Mark maximum and minimum values of the standardized residuals on y axis.

Answer 1

Note : Allowed to solve only 4 sub questions in one post.
a to f has been solved.
Make a scatter plot

Which variable is the predictor or explanatory variable and which is the response variable?

Predictor variable : Penalties
Response variable (dependent variable): Point scored

Conduct a hypothesis test to determine if there is a significant linear correlation
State your null and alternative hypothesis
Justify rejecting or failing to reject the null at the .05 significance level.

Detailed solution for correlation hypothesis testing given below. The correlation value is found in the next calculation.

Provide the equation
Determine r

Detailed steps have been shown.

Find the following statistics

What percent of the variation in points scored is accounted for by the regression equation?

89.48 percent of the variation in points scored is accounted for by the regression equation

Coefficient of determination(rsqaure) = 0.8948
It is the measure of the amount of variability in y explained by x. Its value lies between 0 and 1. Greater the value, better is the model. In this case, it 89.48%, hence the model is good.

In this context we can say that 89.48% of variability in point scored is explained by the penalities.