Can someone help interpret this regression analysis from a dataset? Looking to i
ID: 3320794 • Letter: C
Question
Can someone help interpret this regression analysis from a dataset? Looking to interpret all parameter estimates and determine significance or not at a .10 level.
Variable DF Parameter Estimate Standard Error t-Value Pr > t Intercept 1 2.03704 .17447 11.68 <.0001 Education 1 -0.02041 .00684 -2.98 .0029 Age 1 .00848 .00150 5.67 <.0001 Happy 1 .20211 .03746 5.40 <.0001 Class 1 0.08069 .03876 -2.08 .0376 Income 1 -.00000412 8.545821E-7 -4.82 <0.0001 Smoker 1 -0.17318 .05027 -3.45 .0006Explanation / Answer
The Above table is interpreted below,
The Variable column shows predictor variables (Intercept, Education, Age, Happy, Class, Income and Smoker).
The df denotes degrees of freedom of each variable.
The column Parameter estimates tells you the values for the regression equation for predicting the dependent variable from the independent variable. The regression equation may be like below,
YPredicted = b0+ b1*x1+ b2*x* + b3*x3 + b4*x4 + b5*x5 +b6*x6
The column parameters estimates provides the values for b0, b1, b2, b3, b4, b5 and b4 for this equation.
Education: For every unit increase in education, we expect a -0.02041 unit decrease in the Ypredicted score, holding all other variables constant.
Age: The coefficient for Age is 0.00848. So for every unit increase in education, a 0.00848 unit increase Ypredicted, holding all other variables constant.
Happy: The coefficient for Age is 0.20211. So for every unit increase in education, a 0.20211 unit increase Ypredicted, holding all other variables constant.
Class: The coefficient for Age is 0.08069. So for every unit increase in education, a 0.08069 unit increase Ypredicted, holding all other variables constant.
Income: For every unit increase in education, we expect a -0.00000412 unit decrease in the Ypredicted score, holding all other variables constant.
Smoker: For every unit increase in education, we expect a -0.17318 unit decrease in the Ypredicted score, holding all other variables constant.
The column Standard Error are associated with the coefficients.
The t-value and Pr>t: These are the t-statistics and their associated 2-tailed p-values used in testing whether a given coefficient is significantly different from zero. Using an alpha of 0.10
The coefficient for Education (-0.02041) is statistically significant because p-value of 0.0029 is less than 0.10.
The coefficient for Age (0.00848) is statistically significant because p-value of <0.0001 is less than 0.10.
The coefficient for Happy (0.20211) is statistically significant because p-value of <0.0001 is less than 0.10.
The coefficient for Class (0.08069) is statistically significant because p-value of 0.0376 is less than 0.10.
The coefficient for Income (-0.00000412) is statistically significant because p-value of <0.0001 is less than 0.10.
The coefficient for Smoker (-0.17318) is statistically significant because p-value of 0.0006 is less than 0.10.
The intercept is significantly different from 0 at the 0.10 alpha level.