Regression Help

Question

The following table gives information on the amount of sugar (in grams) and the calorie count in

one serving of a sample of 13 varieties of Kellogg’s cereal.

Sugar (grams)	4	15	12	11	8	6	7	2	7	14	20	3	13
Calories	120	200	140	110	120	80	190	100	120	190	190	110	120

1.     Which is the dependent variable and which is the independent variable?

2.     Do you expect a positive or negative relationship, and why?

3.     If ŷ= 89.4845 + 5.1369x + e, interpret the constant and coefficient of x (slope).

4.     Conduct a test of the research hypothesis that B > 0. Assume t = 3.110 and α = 0.05. Solve this with both the critical value and p-value approach.

5.     Interpret r = 0.6708 and r² = 0.45

Answer 1

1) calories is a function of # of grams of sugar; # of grams of sugar is the independent var;

calories is the dependent

2)

positive expected as calories increase as # of grams of sugar increase

3) slope is 5.1369 and 89.4945+e is the intercept

ŷ = 5.13692X + 89.48425

4) sqrt ( sum of squares of residuals)/(n-2) * [ 1/n + meanX^2/[(n-1)*stndDevX]] = 88.60769

the difference is

doing a reverse table lookup or norminv in Excel, the z-score is < 1.96 at 95% confidence

5) goodness of fit coefficients show that the linear model is not very good