Question

In a regression model with R-squared = 0.829, what should be tested for coefficients b2, b3, and b4?

a) They are zero.
b) They are negative.
c) They are positive.
d) They are non-linear.

Answer 1

In regression analysis with R-squared = 0.829, the coefficients b2, b3, and b4 should be tested to determine if they are statistically different from zero using t-tests. This assesses each coefficient's contribution to the model and their predictive relationship with the dependent variable.

Step-by-step explanation:

In regression analysis, when we have a model with an R-squared value of 0.829, the significant test for the coefficients, such as b2, b3, and b4, is to test whether these coefficients are statistically different from zero. To test this, a t-test is used to determine if each coefficient significantly contributes to the model; in other words, we test the null hypothesis that each coefficient is equal to zero against the alternative hypothesis that it is not.

If the hypothesis test for a specific coefficient is statistically significant, it suggests that there is evidence against the null hypothesis, and the coefficient provides valuable information about the relationship between the independent variable it represents and the dependent variable. If the coefficient is not significantly different from zero, it suggests that the variable may not have a predictive relationship with the dependent variable in the context of the model.