The information below is a regression output examining the relationship between
ID: 3268594 • Letter: T
Question
The information below is a regression output examining the relationship between residential sales prices, measured in dollars "sold_price" and the homes square footage "approx_sqft". Answer the following questions based off the informationDescribe in words what the value of your regression coefficient means. What is the value of your correlation coefficient? What does it mean, in words? Is this believable? Discuss
reg sold price approx_sqft Source I df MS Number of obs3849 F( 1, 3847)= 9700.39 Prob > R-squared Adj R-squared 0.7160 Root MSE 1 6.5211e+14 Residual 2.5861e+14 3847 6.7225e+10 0.0000 -0.7160 Model I 6.5211e+14 Total 9.1072e+14 38482.3667e+11 -2.6e+05 sold price Coef.Std. Err P>It (95% Conf. Interval] 293.0231 -299686 approx sqftI287.304 2.917071 98.49 0.000 281.5848 cons-318043.9 9363.475 -33.97 0.000 -336401.7
Explanation / Answer
1) regression coefficient - when theregression line is linear (y = ax + b) the regression coefficient is the constant (a) that represents the rate of change of one variable (y) as a function of changes in the other (x); it is the slope of the regression line.
So, here regression coefficient is = 287.304
2) R² is the squared multiple correlation coefficient. It is also called the Coefficient of Determination.
So, correlation coefficient here is = 0.7160 = 0.8462 or 84.62%
R, the multiple correlation coefficient and square root of R², is the correlation between the predicted and observed values. In simple linear regression, R will be equal to the magnitude correlation coefficient between X and Y. This is because the predicted values are b0+b1X. Neither multiplying by b1 or adding b0 affects the magnitude of the correlation coefficient. Therefore, the correlation between X and Y will be equal to the correlation between b0+b1X and Y, except for their sign if b1 is negative.
Yes it is believable. It tells there is 84.62% of correlation between predicted and observed values.
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