Question

Discuss the model and interpret the results: report overall model fit (t and significance), report the slope coefficient and significance, report and interpret r squared.

Regression Statistics
Multiple R	0.859343186
R Square	0.738470711
Adjusted R Square	0.737149856
Standard Error	1602.157625
Observations	200

ANOVA
	df	SS	MS	F	Significance F
Regression	1	1435121315	1435121315	559.085376	1.42115E-59
Residual	198	508247993.2	2566909.056
Total	199	1943369308

	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	-1209.21246	444.997983	-2.717343687	0.007164032	-2086.75626	-331.6686596	-2086.75626	-331.6686596
X Variable 1	0.18316543	0.007746481	23.64498628	1.42115E-59	0.167889235	0.198441625	0.167889235	0.198441625

Answer 1

Solution:

Here, we have to discuss the regression model for the prediction of dependent variable y based on the independent variable x. The correlation coefficient between the dependent and independent variable is given as 0.8593 which means there is a strong positive linear relationship exists between the given two variables. The value of the coefficient of determination or the R square is given as 0.7385, which means about 73.85% of the variation in the dependent variable is explained by the independent variable. There are total 200 observations in the given data set. The test statistic value for overall significance of the regression model is given as F = 559.0854 and the p-value for this regression model is given as 0.00 approximately. Here, P-value is less than the significance level or alpha value 0.05, so we reject the null hypothesis. There is sufficient evidence to conclude that the given regression model is statistically significant and we can use this regression model for the prediction of dependent variable y based on the independent variable x. The y-intercept for the regression model or line is given as -1209.2125 and this coefficient is statistically significant as the corresponding p-value is given as 0.0072 which is less than alpha value 0.05. The slope for the regression equation is given as .1832 which is statistically significant because the corresponding p-value is approximately 0.00.