Question

1. The Coefficient of Determination is *

a. the percent of variance in the dependent variable that can be explained by the independent variable

b. the ratio of the variance of Y to the variance of Y for a specific X

c. a measure of how strong the linear relationship is between the explanatory and response variables

2.

The null hypothesis for a regression model is state as *

a. beta_1=0: there is no relationship

b. beta_1 > 0: there is a positive relationship

c. rho=0: there is no relationship

d. rho < 1: there is a negative relationship

3.Choose the best interpretation of \beta_{0} *

a. the sample correlation between x and y

b. the change in y as x increases by 1 unit

c. the amount of uncertainty remaining after fitting the model

d. the value of y when all x's are zero

4.Linear regression analysis is used to assess the relationship between what two types of measurements? *

a. quantiative; quantitative

b. categorical; categorical

c. quantitative; categorical

Answer 1

1. The Coefficient of Determination is:

a. the percent of variance in the dependent variable that can be explained by the independent variable.

>> The coefficient of determination is a measure in regression analysis that assesses how well a model explains and predicts future outcomes. It is the percent of variance in the dependent variable that can be explained by the independent variable. It is also denoted by R-Squared. R-squared is always between 0 and 100%. 0% indicates that the model explains none of the variability of the response data. 100% indicates that the model explains all the variability of the response data. The higher the R-squared, the better the model fits your data.

2. The null hypothesis for a regression model is state as:

a. beta_1=0: there is no relationship

>> Null hypothesis, H0: beta_1 = 0

Alternative hypothesis, H1: beta_1 ≠ 0

3. Choose the best interpretation of beta_0:

d. the value of y when all x's are zero.

>> Regression model: Y = B0 + B1X1 + B2X2 +........+BnXn

When all X's are zero, Y = B0 (beta_0).

4. Linear regression analysis is used to assess the relationship between what two types of measurements:

a. quantitative; quantitative.

>> In linear regression, both dependent variable and independent variables have to numerical or quantitative.