Econometrics Linear regression

• β₁ = 1 as x_i = 1.

One of the assumptions of the classical linear regression model is as follows

• The model assumes that all variables are categorical.
• The relationship between the independent and dependent variables is linear.
• The dependent variable is independent of the independent variables.
• The relationship between the independent and dependent variables is quadratic.

One of the assumptions of the CLRM is as follows:

• Errors are uniformly distributed.
• Errors are always positive.
• Errors are independent of the predictors.
• Error terms are homoscedastic.

To test the null hypothesis that an individual coefficient on explanatory variable in the linear regression model is zero, the test statistic to be used is

• Chi-square test
• F-test
• t-test
• ANOVA

To test the null hypothesis that all coefficients on explanatory variable in the linear regression model are jointly zero, the test statistic to be used is

• F-statistic
• chi-squared statistic
• z-statistic
• t-statistic

The most important measure of the goodness of fit of the linear regression model is

• Mean Squared Error
• Adjusted R-squared
• Standard Deviation
• R-squared

R-squared of the linear regression model can be interpreted as

• The accuracy of the model's predictions.
• The total number of data points used in the model.
• The slope of the regression line.
• The proportion of variation in dependent variable explained by the model.

Adjusted R-squared of a linear regression model is used to

• measure the correlation between variables
• evaluate the goodness of fit of a linear regression model while accounting for the number of predictors
• determine the exact values of coefficients
• predict future outcomes of the model