Stat 301 Lab 7: Due March 25 Spring 2014
1.
The group exercise for Lab 4 looked at the relationship between the temperature of coffee and the time since the coffee was poured. The data consists of the temperature ( o
F) of cups of coffee and the times (minutes) since the coffee was first poured. The data can be considered a random sample of times/temperatures for cups of coffee. The data are given below.
Time Temperature Time Temperature
0
5
179.5
168.7
25
30
123.5
116.3
11
15
22
149.2
141.7
125.4
38
45
50
109.1
102.2
100.5 a) Plot Temperature versus Time. Describe the general pattern. b) Fit a simple linear model relating Temperature to Time.

Give the equation of the least squares line.

Interpret both the estimated intercept and the estimated slope within the context of the problem.

Comment on how well the simple linear model fits the data. Be sure to mention the
R
2
value, RMSE, model utility, significance of variables in the model, and the plot of residuals versus Time. c) Fit a polynomial regression (degree=2) model with Time and Time
2
as the explanatory variables. Do not center variables .

Give the equation of the least squares line.

Give an interpretation of the estimated intercept within the context of the problem.

Why is it difficult to interpret the slope estimates for this model?

Comment on how well the model fits the data. Be sure to mention the R
2
value,
RMSE, model utility, significance of variables in the model, and the plot of residuals versus Time. d) Fit a polynomial regression (degree=3) with Time, Time
2
and Time
3
as the explanatory variables. Do not center variables .

Give the equation of the least squares line.

Comment on how well the model fits the data. Be sure to mention the R
2
value,
RMSE, model utility, and the significance of variables in the model. e) Which model b), c) or d) does a better job of predicting the temperature of coffee after
50 and 60 minutes? Note: This question is not asking which model is the best statistical model but rather which model gives a more realistic prediction for the temperature of coffee after 50 and 60 minutes.
1

f) Report the correlations between Time and Time
2
, Time and Time
3
, Time
2
and Time
3
. Is there statistically significant multicollinearity? Explain briefly. g) Fit a polynomial regression (degree=2) with Time and (Time – Mean Time)
2
.

Give the equation of the least squares line.

Comment on how well the model fits the data. Be sure to mention the R
2
value,
RMSE, model utility, significance of variables in the model, and the plot of residuals versus Time.

How does this model compare to the model in c)? h) Fit a polynomial regression (degree=3) with Time, (Time – Mean Time)
2
and (Time –
Mean Time)
3
as the explanatory variables.

Give the equation of the least squares line.

Comment on how well the model fits the data. Be sure to mention the R
2
value,
RMSE, model utility, and the significance of variables in the model.

How does this model compare to the model in d)? i) Report the correlations between Time and (Time – Mean Time)
2
, Time and (Time –
Mean Time)
3
, (Time – Mean Time)
2
and (Time – Mean Time)
3
. Is there statistically significant multicollinearity? Explain briefly. j) Analyze the residuals from the best polynomial model to see if the conditions for statistical inference are satisfied. Be sure to indicate what the best polynomial model is.
2