Statistics 104 - Laboratory 5
Modeling linear relationships
1. M&Ms
On last week’s lab we looked at data on a random sample of 10 Fun Size bags of M&Ms,
specifically the Total Weight (M&Ms plus bag) and the Number of M&Ms, see table
below.
Bag
Number, x
Total Weight, y
a.
b.
c.
d.
e.
f.
g.
h.
i.
j.
1
2
3
4
5
6
7
8
9
10
22 23 24 21 20 22 21 20 21 21
20 20 21 19 16 17 19 18 19 19
SS(xy) = 12.0
r = 0.7118
Calculate the sample mean and sample standard deviation of the number of
M&Ms in Fun Size bags.
Calculate the sample mean and sample standard deviation of the total weight of
Fun Size bags.
Calculate the least squares regression slope estimate.
Give an interpretation of the slope estimate within the context of the problem.
Calculate the least squares regression y-intercept estimate.
The interpretation of the y-intercept estimate is the predicted value of y (Total
Weight) when x (Number) equals zero. What is the physical interpretation of this
within the context of the problem?
Does the value of the y-intercept estimate seem appropriate given the context of
the problem? Explain briefly.
Use your prediction equation to predict the Total Weight of a Fun Size bag that
contains 24 M&Ms. What is the residual for this prediction?
Put the least squares regression line on the plot of the data. It should be clear that
you have used the regression line to do the plot.
What proportion of the variability in Total Weight is explained by the linear
relationship with Number?
2. Bar of Soap
A high school student in Austrialia collected data on the weight (grams) of a bar of soap
and the number of days since the bar was first used.
Days in use
Weight (g)
1
4
121 103
7
84
9
71
12
50
17
27
20
13
We wish to be able to predict the weight of the bar given the number of days since the bar
1
was first used. Use the JMP output provided below and your knowledge of regression
analysis to answer the following questions.
a. Give the prediction equation for the line relating days in use to weight.
b. Give an interpretation, within the context of the problem, of the estimated slope.
c. Give an interpretation, within the context of the problem, of the estimated yintercept.
d. Use the prediction equation to predict the weight of the bar after 7 days in use.
Also calculate the residual for this prediction.
e. Give the value of R2 and an interpretation of this value.
f. Describe the pattern in the plot of residuals vs. day in use. What does this
indicate about the straight line model for these data?
10.0
150
5.0
Weight
Residual
100
0.0
50
-5.0
0
0
5
15
10
20
25
-10.0
0
Day
5
15
10
20
25
Day
Linear Fit
Weight = 124.53571 - 5.7535714 Day
Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
Parameter Estimates
Term
Estimate
Intercept
124.53571
Day
-5.753571
0.994315
0.993178
3.255654
67
7
Std Error
2.302095
0.194563
t Ratio
54.10
-29.57
Prob>|t|
<.0001
<.0001
2
Statistics 104 - Laboratory 5
Group Answer Sheet
Names of Group Members:
____________________, ____________________
____________________, ____________________
1. M&Ms
a. Sample mean and standard deviation of x, Number.
b. Sample mean and standard deviation of y, Total Weight.
c. Slope estimate.
d. Interpretation of slope estimate.
e. y-intercept estimate.
f. Physical interpretation of y-intercept.
g. Is the value of the y-intercept appropriate?
h. Predicted weight and residual.
3
i. Plot regression line.
Total Weight
25
20
15
15
20
25
Number
j. Proportion of explained variability.
2. Bar of Soap
a. Prediction equation.
b. Interpretation of slope estimate.
c. Interpretaiont of y-intercept estimate.
d. Prediction and residual.
e. Value of R2 and interpretation.
f. Describe pattern of residuals. What does this indicate?
4