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