Question

Do questions E-G

The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 8 varieties of Kellogg’s cereal.

Sugar (grams), ? 4 14 12 10 8 6 7 3

Calories, ? 110 140 130 110 120 100 120 190

a. Construct a scatter diagram for these data. Does the scatter diagram exhibit a linear relationship between the amount of sugar and the number of calories per serving? We want to fit a straight-line model to relate calories y to the amount of sugar x. ? = ?0 + ?1 ? + ?

b. Compute: ????, ????, ????, ?̂ 0, ?̂ 1 .

c. Using your answer in part ( b ), find the predictive regression equation of the number of calories on the amount of sugar. Comment on the direction of the relationship. Does the intercept have a useful interpretation here? Explain.

d. Give a practical interpretation of the value of ?̂ 1. Find the estimated standard error of the regression model and provide an interpretation.

e. For the fifth observation, Compute the predicted value ?̂5, the residual ?̂5.

f. Compute standard error of ?̂ 1 . Find a 97 % Confidence interval for ?1

g. Conduct a test to determine whether the two variables, sugar x and calories y, are positively linearly related. Use ? = 0.05.

Answer 1

Q g) has no positive linearly related because accept H0 and which is correlation is 0

f)conf-interval also given by confint command

e)predict value of fifth observation is 127.5