Example:
Survey
of 3,368 people presented them with 10 different foods
and
asked them to guess at the number of calories.
The
averages of their guesses will be compared to
the
true number of calories using simple linear regression.
|
Food |
TrueCal |
GuessedCal |
|
8oz whole milk |
159 |
196 |
|
5oz spaghetti with tomato sauce |
163 |
394 |
|
5oz macaroni and cheese |
269 |
350 |
|
1 slice wheat bread |
61 |
117 |
|
1 slice white bread |
76 |
136 |
|
2oz candy bar |
260 |
364 |
|
saltine cracker |
12 |
74 |
|
medium apple |
80 |
107 |
|
medium potato |
88 |
160 |
|
twinkie |
160 |
419 |
|
Summary Statistics Correlation: .825 |
Avg: 132.8 Stdev: 84.9 |
Avg: 231.7 Stdev: 134.2 |
Regression Analysis: GuessedCal
versus TrueCal
The
regression equation is
GuessedCal
= 58.59 + 1.304 TrueCal
Predictor Coef
SE Coef T P
Constant 58.59
49.12 1.19 0.267
TrueCal 1.3036
0.3163 4.12 0.003
S =
80.5407 R-Sq = 68.0% R-Sq(adj) = 64.0%
Analysis
of Variance
Source DF
SS MS F
P
Regression 1
110176 110176 16.98
0.003
Error 8
51894 6487
Total 9
162070
Predicted
Values for New Observations
NewObs Fit
SE Fit 95% CI 95% PI
1
241.1 25.6 (182.1, 300.1) (46.2, 435.9)
Values
of Predictors for New Observations
NewObs TrueCal
1
140
Predicted
Values for New Observations
NewObs Fit
SE Fit 95% CI 95% PI
1 384.5 45.0 (280.8, 488.2) (171.8, 597.2)
Values
of Predictors for New Observations
NewObs TrueCal
1
250