Question 1 Study the following Minitab output from a regression analysis to predict y from x a. What is the equation of the regression model? b. What is the meaning of the coefficient of x? c. what is the result of the test of the slope of the regression model? Let a = .10·Why is the t ratio negative? d. Comment on and the standard error of the estimate e. Comment on the relationship of the F value to the t ratio forx f. The correlation coefficient for these two variables is -0.7918. Is this result surprising to you? Why or why not? Regression Analysis: Y versus X The regression equation is Y= 67.20-0.0565 X Coef 67.231 0.05650 R-Sq=62.7% SE Coef 5.046 0.01027 R-Sq(adj)= Predictor Constant 13.32 0.000 5.50 0.000 S = 10.32 60.6% Analysis of Variance Source Regression Residual Error Total DF MS 30.25 0.000 3,222.9 3,222.9 1,918.0 106.6 5,141.0 18 19 (Round your answer to 1 decimal places.) (Round your answer to 4 decimal places.) Round your answer to 2 decimal places.) a. The regression equation is: b. For every unit of increase in the value of x, the predicted value of y will by KX
A ) The regression equation is
B ) The coefficient of x represents the slope of regression line
Interpretation of Slope : For every unit increase in x the predicted value of y decreases by 0.0565 units
C ) the t ratio of the slope is -5.50 with the associated pvalue 0.000
i.e. we can conclude that the slope is significant.
D ) R^2 =62.70% of the variability of y is accounted by x . This is explained variability in y explained by x.
Standard error of the estimate is 1918
E ) The F value owhich test the overall predictability of the model is 30.25
The correlation coefficient for this two variables is -0.7918 .
i.e. correlation coefficient is less than 0 , So , there is negative correlation between this two variables.
The -0.7918 is not surprising because the slope of the regression line is also -0.0565 indicating an NEGATIVE relationship between x and y.