SUMMARY OUTPUT
Regression Statistics
Multiple R 0.903696
R Square 0.816667
0.725
Adjusted R Square
7.416198
Standard Error
Observations 4
ANOVA
df SS MS F Significance F
Regression 1 490 490 8.909091 0.096304
Residual 2 110 55
Total 3 600
Standard Error t Stat
Coefficients P-value Lower 95%Upper 95% Upper 95.0%
Lower 95.0%
Intercept 59 7.952987 7.418596 0.017689 24.78104 93.21896 24.78104 93.21896
Fertilizer (X) in lbs. 7 2.345208 2.98481 0.096304 -3.09062 17.09062 -3.09062 17.09062
RESIDUAL OUTPUT
Predicted in lbs. Standard Residuals
Observation Yield (Y) Residuals
1 66 4 0.660578
2 73 -3 -0.49543
3 87 -7 -1.15601
4 94 6 0.990867
Fertilizer (X) in lbs. Residual Plot
10 Fertilizer (X) in lbs. Line Fit Plot
Residuals
5 Yield (Y) in lbs.
0 150
-5 0 100 2 4 6
Yield (Y) in lbs.
-10 50
0
Fertilizer (X) in lbs. Predicted Yield (Y) in
0 5 10
lbs.
Fertilizer (X) in lbs.
Upper 95.0%
Fertilizer and Radioactivity Regression Examples Fertilizer: Sheet 1
Fertilizer (X) in lbs. Yield (Y) in lbs. X-mean Y-mean Cross Products Squared (X-mean)
1 70 -2 -10 20 4
2 70 -1 -10 10 1
4 80 1 0 0 1
5 100 2 20 40 4
Mean of X Mean of Y Sum Sum Sum Sum
3 80 0 0 70 10
Y=B0 + B1X variance of Y
B0 = Ymean - B1Xmean
B1 = (Sum of Cross Products)/Sum of Squared(X-mean)
B1 B0
7 59
Radioactivity: Sheet 2
Fitted y
Squared (Y-mean) Resid Fitted Squared y-hat - mean
squared resids deviation
100 66 4 16 -14 196
100 73 -3 9 -7 49
0 87 -7 49 7 49
400 94 6 36 14 196
80
600 320 0 110 0 490
200
0.816667
0.816667
Yield (Y) in lbs. y = 7x + 59
R² = 0.8167
120
100
Pounds of Corn
80
60
40 Yield (Y) in lbs.
20 y = 7x + 59
120 R² = 0.8167
0
100
0 1 2 3 4 5
Pounds of Corn
80 Pounds of Fertilizer Yield (Y) in lbs.
60
Linear (Yield (Y) in
40 lbs.)
20
0
0 2 4 6
Pounds of Fertilizer
y = 7x + 59
R² = 0.8167
R² = 0.8167
6
Yield (Y) in lbs.
Linear (Yield (Y) in
1950s Radioactive Waste Leaked in Washington into the Columbia River
County Exposure Cancer Mortality
8.3 210
6.4 180
3.4 130
3.8 170
2.6 130
11.6 210
1.2 120
2.5 150
1.6 140