DATA y x1 10 2113 11 2003 11 2957 13 2285 10 2971 11 2309 10 2528 11 2147 4 1689

Question

DATA

y x1

10 2113

11 2003

11 2957

13 2285

10 2971

11 2309

10 2528

11 2147

4 1689

2 2566

7 2363

10 2109

9 2295

9 1932

6 2213

5 1722

5 1498

5 1873

6 2118

4 1775

3 1904

3 1929

4 2080

10 2301

6 2040

8 2447

2 1416

0 1503

e. Find a 99% Confidence Interval for the mean number of games won if the team has 2000 f. Interpret (in words, with complete sentences) what the confidence interval obtained in g. what is a 99% confidence interval for the number of games won if an individual team h. Discuss the residual plots. Specifically, do the four underlying assumptions to linear yards rushing (i.e., xi- 2000). part e means has 2000 yards rushing? regression seem to be valid? Present SPECIFIC characteristics of the plots to support your assertions.

Explanation / Answer

a. A confidence interval is an interval in which there is maximum probability of a parameter, of the population falling in this case being the mean.

Since in this case there we have only the sample, we should first calculate the standard deviation s of the sample, The number of observation points = n, the confidence level is at 99% i.e alpha = 0.01

So the formula to calculate this interval is

xbar +- t(alpha/2) * (s/SQRT(n)) where xbar = 2000 and t is the vlaue of the area under the st. normal curve to the right of t = 0.005

Substituting all the values we can get the 99% C.I. around x = 2000

b. A confidence interval is an interval in which there is maximum probability of a parameter, of the population falling in this case being the mean. So if we want to be 95 % sure that the range within which the mean of the population in this case will fall, then we construct a 95% confidence interval around the mean calculated from the smaller sample size which we have in this case.

So the 99% confidence interval is a projection of where the population parameter will fall

c. A 99% confidence interval for the number of games won by a team when x = 2000 is related to the linear model

A linear model helps predict the dependent variable given a certain value of the independent variable, but this prediction is not always true and has a certain error associated with it which depends on the fit of the model.

So a 99% confidence interval is an interval around the predicted value at x = 2000, where we are 99% confident that the actual observed value will lie irrespective of error of the model

d. Yes the residual plots shown do indicate a linear model, which can be built by a linear regression model. For example the residual versus percent plot is a straight line passing through most points and the residual vs frequecy plot, indicates a constant deviation of -2 for majority of the points which means that many of the underlying assumptions to linear regression seem to be true

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