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