Homework 1
HW1, Spring 2013
Regression Analysis (STAT338)
Please solve the following exercise and submit a group solution on Tuesday, 27 February 2013.
The strength of paper (y) used in the manufacture of cardboard boxes is related to the percent of hardwood concentration (x) in the original pulp. Under uncontrolled conditions, a pilot plan manufacturers 16 samples, each from a different batch of pulp, and measured the tensile strength. The data are shown below.
Strength of paper Percent of hardwood concentration
1.0 101.4
1.5 117.4
1.5 117.1
1.5 106.2
2.0 131.9
2.0 146.9
2.2 146.8
2.4 133.9
2.5 111.0
2.5 123.0
a) Find the correlation coefficient between strength of paper and percentage of hardwood concentration. Comment on the strength, direction and form of the relationship.
b) Draw a scatterplot and comment on the relationship between strength and percent of hardwood concentration.
b) Fit a simple linear regression model to the data and interpret the coefficients.
c) Predict the strength of paper of a cardboard box if the percent of hardwood concentration in the original pulp is 2.6.
d) Predict with 95% confidence the strength of paper of a cardboard box if the percent of hardwood concentration in the original pulp is 2.6.
e) Estimate with 95% confidence the mean strength of papers of cardboard box if the percent of hardwood concentration in the original pulp is 2.6.
f) Find the coefficient of determination (R2) and comment. Based on R2 value is the model a good one?
g) At the 5% significance level, do the data provide sufficient evidence to conclude that there is a significant relationship between percent of hardwood concentration in the original pulp and strength of paper of the cardboard box?
h) Check the assumptions of the fitted
Regression Analysis (STAT338)
Please solve the following exercise and submit a group solution on Tuesday, 27 February 2013.
The strength of paper (y) used in the manufacture of cardboard boxes is related to the percent of hardwood concentration (x) in the original pulp. Under uncontrolled conditions, a pilot plan manufacturers 16 samples, each from a different batch of pulp, and measured the tensile strength. The data are shown below.
Strength of paper Percent of hardwood concentration
1.0 101.4
1.5 117.4
1.5 117.1
1.5 106.2
2.0 131.9
2.0 146.9
2.2 146.8
2.4 133.9
2.5 111.0
2.5 123.0
a) Find the correlation coefficient between strength of paper and percentage of hardwood concentration. Comment on the strength, direction and form of the relationship.
b) Draw a scatterplot and comment on the relationship between strength and percent of hardwood concentration.
b) Fit a simple linear regression model to the data and interpret the coefficients.
c) Predict the strength of paper of a cardboard box if the percent of hardwood concentration in the original pulp is 2.6.
d) Predict with 95% confidence the strength of paper of a cardboard box if the percent of hardwood concentration in the original pulp is 2.6.
e) Estimate with 95% confidence the mean strength of papers of cardboard box if the percent of hardwood concentration in the original pulp is 2.6.
f) Find the coefficient of determination (R2) and comment. Based on R2 value is the model a good one?
g) At the 5% significance level, do the data provide sufficient evidence to conclude that there is a significant relationship between percent of hardwood concentration in the original pulp and strength of paper of the cardboard box?
h) Check the assumptions of the fitted