Question

1. If the linear correlation coefficient of two variables is zero, then there is no _______________ relationship between the variables. A linear correlation coefficient of 0.92 suggests a ________________ linear relationship than a linear correlation coefficient of -0.86. The value of the ___________________ always lies between -1 and 1, inclusive. If the linear correlation coefficient of the regression line is negative, then the ____________________ of the least squares (linear) regression line must be negative. Give a detailed interpretation of the slope of a least squares (linear) regression line. Give a detailed interpretation of the intercept of a least squares (linear) regression line. Give a detailed interpretation of the coefficient of determination (R^2). Give two different methods to determine if a linear regression line fits data best. Describe in detail within each method what trends or information would constitute a lack of fit for any linear regression model.

Answer 1

The linear correlation coefficient lies between -1 and +1, the closer it is to -1, the more it has a negative linear relationship between the two variables. While the closer it is to +1, the more it has a positive correlation between the two variables. Also a value closer to 0 means no correlationship between the two variables.

Now we fill the blanks here as:

If the linear correlation coefficient of two variables is zero, then there is no linear relationship between the variables. A linear correlation coefficient of 0.92 suggests a positive linear relationship than a linear correlation coefficient of -0.86. The value of the linear correlation coefficient always lies between -1 and 1, inclusive. If the linear correlation coefficient of the regression line is negative, then the slope of the least squares (linear) regression line must be negative.

• The interpretation of the slope is that for a unit increase in value of independent variable, the expected increase in the value of dependent variable value is equal to the slope while a unit decrease would lead to a slope decrease to dependent variable.
• The interpretation of the intercept is that for 0 value of the independent variable, the expected value of the dependent variable would be equal to the intercept.
• The coefficient of determination is defined as the proportion of variation in the dependent variable that is explained by the variation in the independent variable or explained by regression.
• To test whether a linear regression fit the data, we can use the t test for testing the significance of the independent variables. In the same way, we use the correlation coefficient to determine the strength of linear correlation between the two variables.