Question

# Question 1: The data table shows the sugar content of a fruit (Sugar) for different numbers...

Question 1:

The data table shows the sugar content of a fruit (Sugar) for different numbers of days after picking (Days).

 Days Sugar 0 7.9 1 12.0 3 9.5 4 11.3 5 11.8 6 10.3 7 4.2 8 0.8

HAND CALCULATIONS:

The dependent (Y) variable is sugar content and the independent (X) variable is number of days after picking (Days).

Do the following by hand, SHOWING WORK. You may use SAS/R to check your answers if you want.

(a) Find S_yy, S_xx and S_xy. Use these to calculate the estimated least-squares line

and to find SSE and MSE.

(b) Find a 95% confidence interval for the true slope of the regression. Interpret the interval

in the context of the variables in the problem.

(c) Find the residual for the first observation in the data set.

(d) Find a 95% prediction interval for the sugar content of a fruit (Sugar) having 2 picking days

COMPUTER CALCULATIONS:

Question 2

Look at the data in Table 7.18 on page 368 of the textbook. These data are also

given in the SAS code labeled “SAS_basketball_goal_data” and R code labeled basketball goal data .

The dependent variable is goals and the independent variable is height of basketball players.

Complete a SAS /R program and answer the following questions about the data set:

(a) Does a scatter plot indicate a linear relationship between the two variables?

Is there anything disconcerting about the scatter plot? Explain.

(b) Fit the least-squares regression line (using SAS / R) and interpret the estimated slope

in the context of this data set. Does it make sense to interpret the estimated intercept? Explain.

(c) For these data, what is the unbiased estimate of the error variance? (Give a number.)

(d) Using the SAS / R output, test the hypothesis that the true slope of the regression line

is zero (as opposed to nonzero). State the appropriate null and alternative hypotheses,

give the value of the test statistic and give the appropriate P-value. (Use significance

level of 0.05.) Explain what this means in terms of the relationship between the two

variables.

(e) Using SAS / R, find a 95% confidence interval for the mean basketball goal for

a player with a height of 77 inches. In addition find a 95% prediction interval for

basketball goal for a player with a height of 77 inches.

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