Question

The data from exercise 1 follow.



The estimated regression equation for these data is yˆ = .20 + 2.60x.
Compute SSE, SST, and SSR using the following equations (14.8), (14.9), and (14.10) (to 1 decimal if necessary).



SSE
SST
SSR


Compute the coefficient of determination r2 (to 3 decimals).


Does this least squares line provide a good fit?


Compute the sample correlation coefficient (to 4 decimals).

Answer 1

Concepts and reason

Regression: Regression is a technique that is used to determine relationship between two or more variables. That is, the change in the predictor variable influences the change in the dependent variable is determined. Moreover, in regression analysis which involves more than one independent variable, the change in the dependent is analyzed when the one independent variable is varied by keeping all other independent variables as constant.

Slope: The slope of a least squares regression line is interpreted as the predicted change in the average response variable for a one-unit change in the explanatory variable.

Intercept: The y-intercept of a regression line is interpreted as the predicted value of the response variable when the explanatory variable has a value of zero.

Coefficient of determination: The coefficient of determination is the percentage of total observed variation in theresponse variable that is accounted for by changes (variability) in the explanatory variable.

Residual: A residual is the difference between an observed response and the corresponding prediction made by the least squares regression line (residual = observed- predicted). Thus, negative residuals occur when points are below the best fit line and positive residuals occur when points are above the best fit line.

Correlation:

A statistical method that is applied between the pairs of variables to check how the strongly they are related is termed as correlation. The correlation measures the two given variables based on,

Strength of the association

Direction of the relationship

Strength of the association: The correlation between the two variables x and y take values between 1 and +1.

Direction of the relationship: Based on the sign of the correlation the direction of the relationship is identified between the two variables. Also, the signs may be positive or negative.

Fundamentals

If the data set is bivariate, then linear regression best suits the data. The straight line known as least squares regression line is obtained which best represents the data with two variables. The equation of the line is given by,