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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)4151211867271420313Calories12020014011012080190100120190190110120
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
Solution
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