data
y | x1 | x2 |
8 | 3 | 3.6 |
9 | 3 | 3.3 |
8 | 3 | 3.8 |
4 | 2 | 3.6 |
2 | 2 | 3.6 |
2 | 2 | 3.5 |
6 | 3 | 4.3 |
11 | 3 | 4.2 |
16 | 5 | 4.5 |
15 | 4 | 4.1 |
15 | 4 | 4.1 |
14 | 3 | 3.3 |
13 | 3 | 3.2 |
10 | 3 | 3.4 |
Excel
data -> data analysis -> regression
SUMMARY OUTPUT | |||||
Regression Statistics | |||||
Multiple R | 0.913624328 | ||||
R Square | 0.834709413 | ||||
Adjusted R Square | 0.804656579 | ||||
Standard Error | 2.114322363 | ||||
Observations | 14 | ||||
ANOVA | |||||
df | SS | MS | F | Significance F | |
Regression | 2 | 248.3260504 | 124.1630252 | 27.77473213 | 5.01608E-05 |
Residual | 11 | 49.17394958 | 4.470359053 | ||
Total | 13 | 297.5 | |||
Coefficients | Standard Error | t Stat | P-value | Lower 95% | |
Intercept | 6.279831933 | 5.445721818 | 1.153167962 | 0.273283902 | -5.706120975 |
x1 | 6.311764706 | 0.893113823 | 7.067144792 | 2.07978E-05 | 4.346034434 |
x2 | -4.31092437 | 1.769322904 | -2.436482544 | 0.033028029 | -8.205177825 |
3)
y^= 6.2798 + 6.3118 x1 -4.3109 x2
4)
r^2 = 0.8347
which means 83.47 % of variation in y is explained by this
model
r = 0.9136
adjusted r^2 = 0.8047
alpha = 0.05
p-value of x1 = 0.00002 < alpha , hence x1 is significant
p-value of x2 = 0.033 < alpha , hence x2 is also significant
F-value = 27.7747
p-value of model is 0.00005 < alpha
hence the model is significant
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