Question 3 The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 6 varieties of granola bars. Sugar (grams) Calories 4 12 8 7 14 6 120 140 120 180 190 80 a. Decide which variable should be the independent variable and which should be the dependent variable. Justify your decision. (2 marks) b. Compute X,ΣX², EY, Y² and XY (5 marks) c. Find and interpret the slope of the regression line. (3 marks) d. Find and interpret the intercept of the regression line. (3 marks) e. Write down the regression equation. (1 mark) f. Find and interpret the coefficient of determination. (3 marks) g. Use the 10% level of significance to examine whether the independent variable is a good predictor for the dependent variable. In responding, state the null hypothesis(es), the decision rule and make the decision for each hypothesis. (5 marks) h. Would the simple regression be useful in predicting calories given the amount of sugar of i. 5 grams? In responding, state the null hypothesis(es), the decision rule for α = 0.05 and make the decision for each hypothesis. (5 marks) Find and interpret a 90% confidence interval for the slope of the regression line. (4 marks) j. Find and interpret a 95% confidence interval for the calories when the the amount of sugar is 10 grams. (4 marks) TOTAL: 95 MARKS
Question 3 The following table gives information on the amount of sugar (in grams) and the calorie count in one serving of a sample of 6 varieties of granola bars. Sugar (grams) Calories 4 12 8 7 14 6 120 140 120 180 190 80 a. Decide which variable should be the independent variable and which should be the dependent variable. Justify your decision. (2 marks) b. Compute X,ΣX², EY, Y² and XY (5 marks) c. Find and interpret the slope of the regression line. (3 marks) d. Find and interpret the intercept of the regression line. (3 marks) e. Write down the regression equation. (1 mark) f. Find and interpret the coefficient of determination. (3 marks) g. Use the 10% level of significance to examine whether the independent variable is a good predictor for the dependent variable. In responding, state the null hypothesis(es), the decision rule and make the decision for each hypothesis. (5 marks) h. Would the simple regression be useful in predicting calories given the amount of sugar of i. 5 grams? In responding, state the null hypothesis(es), the decision rule for α = 0.05 and make the decision for each hypothesis. (5 marks) Find and interpret a 90% confidence interval for the slope of the regression line. (4 marks) j. Find and interpret a 95% confidence interval for the calories when the the amount of sugar is 10 grams. (4 marks) TOTAL: 95 MARKS
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Transcribed Image Text:Question 3
The following table gives information on the amount of sugar (in grams) and the calorie count in
one serving of a sample of 6 varieties of granola bars.
Sugar (grams)
Calories
4
12
8
7
14
6
120
140
120
180
190
80
a. Decide which variable should be the independent variable and which should be the
dependent variable. Justify your decision. (2 marks)
b. Compute X,ΣX², EY, Y² and XY (5 marks)
c. Find and interpret the slope of the regression line. (3 marks)
d. Find and interpret the intercept of the regression line. (3 marks)
e. Write down the regression equation. (1 mark)
f. Find and interpret the coefficient of determination. (3 marks)
g. Use the 10% level of significance to examine whether the independent variable is a good
predictor for the dependent variable. In responding, state the null hypothesis(es), the
decision rule and make the decision for each hypothesis. (5 marks)
h. Would the simple regression be useful in predicting calories given the amount of sugar of
i.
5 grams? In responding, state the null hypothesis(es), the decision rule for α = 0.05 and
make the decision for each hypothesis. (5 marks)
Find and interpret a 90% confidence interval for the slope of the regression line. (4 marks)
j. Find and interpret a 95% confidence interval for the calories when the the amount of sugar
is 10 grams. (4 marks)
TOTAL: 95 MARKS
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