Regression Analysis: Y versus X The regression equation is Y= 67.2-0.0565 X Pred
ID: 3327446 • Letter: R
Question
Regression Analysis: Y versus X The regression equation is Y= 67.2-0.0565 X Predictor Coef Constant 67.231 5.046 13.32 0.000 SE Coef -0.05650 0.01027-5.50 0.000 S= 10.32 R-Sq 62.7% R-Sq (adj) = 60.6% = Analysis of Variance Source Regression Residual Error 18 1918.0 106.6 Total DE SS MS 1 3222.9 3222.9 30.25 0.000 19 5141.0 a. What is the equation of the regression model? (1 marks) b. What is the meaning of the coefficient of x? (2 marks) c-what is the result of the test of the slope of the regression model? alpha = 0.10. why is the t ratio negative? (5 marks) d. Comment on rz and the standard error of the estimate. (2 marks) e. Comment on the relationship of the F value to the t ratio for x. (5 marks) f. The correlation coefficient for these two variables is -.7918. Is this result surprising to you? Why or why not?Explanation / Answer
Answer to the questions here:
a. Equation: y = 67.231 -.05650*X
b. It means that per unit increase of X there is a decrease of y by .05650 units
c. Result of slope is that it is significant as it' p-value is less than .05. Also, -ive t value depicts negative coefficient, ie. opposite relation between y and x
d. rsquare is at 62.7%, indicating not a decent relation between y and x. Its' not so strong enough. SE is low at 10.21, indicating a decent fit of line to the points.
e. F ratio of 30.25 has p-value of 0.00, indicating a significant linear regreesion equation as p-value is less than .05
f. No. it doesn't . It a decent correlation value, though in opposite direction. i.e. it means that y varies opposite of x