Suppose You Are Testing the Null Hypothesis That the Slope

question 76

Multiple Choice

Suppose you are testing the null hypothesis that the slope of the regression line is zero versus the alternative hypothesis that the slope is different than zero.Would a very small P-value indicate a strong relationship between the explanatory variable and the response variable?

• A)Yes,because the P-value will give the strength of the association between the explanatory variable and the response variable
• B)Yes,because if the P-value is small,then R² is large
• C)No,because there could be a lot of scatter about the regression line,indicating a weak fit of the data to the model
• D)No,because a large P-value would indicate a strong relationship between the explanatory variable and the response variable

---

Definitions:

Curvilinear Regression

A statistical technique used to model the relationship between a dependent variable and one or more independent variables where the relationship is not linear.

Coefficient Of Determination

A statistical measure represented as R² that assesses the proportion of the variance in one variable that is predictable from the other variable.

Standard Error Of The Estimate

A measure of the accuracy of predictions made by a regression line, indicating the standard deviation of the residuals.

Adjusted R Square

A statistical measure that indicates the proportion of the variance in the dependent variable that is predictable from the independent variables, adjusted for the number of predictors in the model.