Y x1 x2
57 220 125
43 216 147
73 250 118
37 241 160
64 305 128
48 258 149
56 354 145
50 321 150
39 370 140
43 375 115
69 385 155
60 385 152
Calculate
1, the coefficient of multiple determination
2,test for individual coefficients
3,test the over all significant of the model
To calculate the coefficient of multiple determination (R^2):
1. Calculate the sum of squares total (SST):
SST = Σ(yi - ȳ)^2
where yi is the actual value of the dependent variable and ȳ is the mean of the dependent variable.
2. Calculate the sum of squares residual (SSE):
SSE = Σ(yi - ŷi)^2
where ŷi is the predicted value of the dependent variable using the regression equation.
3. Calculate the coefficient of multiple determination (R^2):
R^2 = 1 - (SSE/SST)
To test for individual coefficients, you can use the t-test. The t-test compares the calculated t-value for each coefficient against a critical t-value at a specific significance level. If the calculated t-value is greater than the critical t-value, then the coefficient is considered significant.
To test the overall significance of the model, you can use the F-test. The F-test compares the calculated F-value, which is calculated using the mean squared regression (MSR) and mean squared error (MSE), against a critical F-value at a specific significance level. If the calculated F-value is greater than the critical F-value, then the model is considered significant.
Please provide the regression equation (if available) so we can provide more specific calculations.