Stat 101L: Lecture 16
Goal 3 – Straighten Up
 What
is the relationship
between the temperature of
coffee and the time since it
was poured?
–Y, temperature ( oF)
–X, time (minutes)
1
Bivariate Fit of Temp By Time (min)
200
190
180
170
Temp
160
150
140
130
120
110
100
90
80
0
10
20
30
40
50
60
Time (min)
2
Cooling Coffee
 There
is a general negative
association – as time since the
coffee was poured increases
the temperature of the coffee
decreases.
3
1
Stat 101L: Lecture 16
Linear Model
190
180
Temp (F)
170
160
150
140
130
120
110
100
-10
0
10
20
30
40
50
60
Time (min)
4
Linear Model Fit
 Summary
– Predicted Temp = 176.7 –
1.56*Time
– On average, temperature decreases
1.56 oF per minute.
– R2 = 0.99, 99% of the variation in
temperature is explained by the
linear relationship with time.
5
Plot of Residuals
5
4
3
Residual
2
1
0
-1
-2
-3
-4
-5
-10
0
10
20
30
40
50
60
Time (min)
6
2
Stat 101L: Lecture 16
Curved Pattern
 There
is a clear pattern in the
plot of residuals versus time.
–Under predict, over predict,
under predict.
 The
linear fit is very good, but
we can do better.
7
Bivariate Fit of Log(Temp) By Time (min)
5.5
5.4
5.3
Log(Temp)
5.2
5.1
5
4.9
4.8
4.7
4.6
4.5
-10
0
10
20
30
40
50
60
Time (min)
Linear Fit
8
Log(Temp) by Time
 Summary
– Predicted Log(Temp) = 5.1946 –
0.0114*Time
–On average, log temperature
decreases 0.0114 log(oF) per
minute.
9
3
Stat 101L: Lecture 16
Plot of Residuals
0.010
Residual
0.005
0.000
-0.005
-0.010
-10
0
10
20
30
40
50
60
Time (min)
10
Interpretation
 There
is a random scatter of
points around the zero line.
 The linear model relating
Log(Temp) to Time is the best
we can do.
11
Original Scale?
 Predicted
Log(Temp) = 5.1946 –
0.0114*Time
 Predicted Temp =
180.3*e–0.0114*Time
– Predicted temp at time=0, 180.3 oF
– The predicted temp in one more minute
is the predicted temp now multiplied by
e–0.0114 = 0.98866
12
4
Stat 101L: Lecture 16
JMP
 Method
1
–Create a new column in JMP,
Log(Temp): Cols – Formula –
Transcendental – Log.
13
JMP
 Method
1 (continued)
–Fit Y by X
Y
– Log(Temp)
X – Time
–Fit Linear
14
JMP
 Method
2
–Fit Y by X
Y
– Temp
X – Time
–Fit Special
Transform
Y – Log
15
5