Question

 

c. Based upon the output, please do the following:

            1) write out the estimated equation.

Y=243.13+1.2X

            2) predict the next value in the time series.

Y=243.13+1.2(121)=388.33

            3) interpret the slope coefficient for time.

            4) test whether or not there is an upward trend in the dependent variable.

                Use alpha = 0.05.

            5) identify the value of the p-value for the model test.

            6) interpret the coefficient of determination for the model.

7) test whether or not the model has explanatory power. Use alpha = 0.05.

            8) construct and interpret a 98% confidence interval for the population slope

                coefficient.

            9) what is the residual for the February of year 3.

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.69242671
R Square	0.47945475			388.33
Adjusted R Square	0.47500565
Standard Error	43.2964202
Observations	119
ANOVA
	df	SS	MS	F	Significance F
Regression	1	202012.846	202012.846	107.764323	2.7258E-18
Residual	117	219325.86	1874.58
Total	118	421338.706
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	243.128871	8.08872102	30.0577644	7.3616E-57	227.109582	259.148159	227.109582	259.148159
1	1.19943028	0.11554137	10.3809597	2.7258E-18	0.97060666	1.42825391	0.97060666	1.42825391

Answer 1

c. Based upon the output, please do the following:

            1) write out the estimated equation.

Sol: The estimated equation is:

Y = 243.1289+1.1994*X

            2) predict the next value in the time series.

Sol: we are supposed to predict the next value in time series. There are 119 observations in the data, hence next value for X = 120. The above equation can be solved for X=120.

Y = 243.1289+1.1994*120=387.0569

3) interpret the slope coefficient for time.

Sol: The slope for above equation is 1.1994. This is positive value, hence we can conclude that there is positive correlation between dependent and independent variable. We can also conclude that there is 1.1994 change per unit change in dependent variable for one unit change in Time (x).

            4) test whether or not there is an upward trend in the dependent variable.

                Use alpha = 0.05.

Sol: The p-value for test for trend is nothing but the p-value for ANOVA. Here the P-value is 2.73E-18. Hence we reject the null hypothesis at 5% and conclude that there is statistically significant linear trend in the data.

            5) identify the value of the p-value for the model test.

Sol: The p-value for the model test is the p-value corresponding to ANOVA i.e. P=2.73E-18