stats final

What does a significant Chi-Square (χ²) value suggest about variables?

It suggests that a relationship exists between the variables.

What does the Phi (φ) Coefficient measure?

It measures the strength of the relationship in 2x2 tables.

What are the key components of the regression equation?

Y = a + bX + e, where a is the intercept, b is the slope, and e is the error term.

What does R² (Coefficient of Determination) indicate in multiple regression?

It indicates the proportion of variance in the dependent variable explained by the independent variables.

What is the null hypothesis for the slope in regression analysis?

The null hypothesis states that the slope is zero, indicating no relationship.

What is the purpose of the t-test in regression analysis?

To evaluate whether the observed slope differs significantly from zero.

What does a p-value less than 0.05 imply in regression?

It implies that the predictor has a statistically significant effect.

How is an interaction term represented in regression modeling?

As the product of two predictor variables, e.g., X1×X2.

What is the function of the intercept (a) in a regression model?

It represents the predicted value of the dependent variable when the independent variable is zero.

What are the assumptions necessary for a regression analysis to be valid?

Linearity, homoscedasticity, normality of residuals, and independence of errors.

What is covariance in the context of regression analysis?

It measures how much two variables change together.

What is the significance of statistical interaction in regression models?

It shows that the effect of one predictor depends on the level of another predictor.

How does the magnitude of a regression slope relate to the relationship between variables?

It reflects the strength of the relationship; a larger magnitude indicates a stronger relationship.

What is the role of the residuals in regression analysis?

Residuals are the differences between observed and predicted values; they help assess model fit.

What does a positive slope in regression indicate?

As the independent variable increases, the dependent variable also increases.

What is the definition of the coefficient of determination (R²)?

R² is the square of Pearson’s r, representing the proportion of variance in the dependent variable explained by the independent variable.