Question

You conducted a regression analysis between Amount of Wealth in society (x) and the Stock Market Value (y) and the study yielded the following results. The r = 0.5, the Y intercept when x = 0 is 42, the slope of the regression line is 3. Using problem 1.4 you conducted further analysis and found out that the r = 0.80.

What is the R-Squared and what does it say about the previous regression you conducted?

a. The R-squared is 0.64 and it means that the independent value explains 64% of the dependent value in the simple regression analysis
b. The R-squared is 1.6 and it means that I am 160% sure the regression is correct
c. The R-squared is 1.6 and it means that 160% of the variation in the stock market can be explained by the variation in the Wealth of Society
d. The R-squared is 1.6 and it means that 160% of the variation in the dependent value (y) can be explained by the variation in the independent value (x)
e. The R-squared is 0.64 and it means that the dependent value explains 64% of the independent value in the simple regression analysis

Answer 1

E IS THE CORRECT ANSWER

The R-squared is 0.64 and it means that the dependent value explains 64% of the independent value in the simple regression analysis

Explanation:

R-Squared value is a very important indicator in a regression analysis.

What does it measure?

It measures how close to the line of best fit are the data points. How good the fitted line is can be indicated by the value of the r-squared.

The maximum value it can take is 1 and at this value, there is a direct and complete relationship between the independent variable x and the dependent variable y. The value 1 represents an 100% relationship between both parties.

The r-squared has a value of between 0 and 100%. The closer to 100, the better the model while the closer to 100, the more faulty the model is. In fact, a value of 0 indicates no relationship at all between the dependent and the independent variable.

With an R-squared value of 0.64, the regression model works above average to explain that the dependent variable explains 64% of the independent value in the simple regression analysis.