Question

Distance (air miles) Fare (dollars) An air travel service is interested in the relationship between distance and airfare. Using distance as the independent variable and an alpha level of .05 answer the following: 636 109 2395 252 2176 221 605 151 403 138 1258 209 264 254 627 259 2342 215 177 128 2521 348 1050 224 441 175 1021 256 336 121 752 252 1333 206 1460 167 2350 308 621 152 737 175 853 191 1894 231 2465 251 1891 291 1028 260 545 123 1489 211 452 139 969 243 a. Write the regression equation. b. Interpret the regression constant and coefficient. c. Forecast a value for the airfare. d. Test the significance of the regression model. e. Test the significance of the regression coefficient. f. Interpret the coefficient of determination. g. Are there any violations of the general linear model?

Answer 1

(a) the regression equation is Fare(y)=147.0812+0.0527*Distance(x)

(b) constant=147.0812 is the amount of fare when distance=0,

coefficient=0.0527 is amount of fare when unit distance is changed

(c) let the we want to forecast for a distance x=1000, then fare ==147.0812+0.0527*1000=199.7812

(d) since the p-value =8.41E-05 is less than the typical alpha=0.05, is regression model is significant

(e) since the p-value of the distance 8.41E-05 is less than the typical alpha=0.05, is coefficient model is significant

and same interpretation for intercept(or constant)

(f) coefficient of determination R-square=0.4297 is the proportion of variation in the dependent variable FARE explained by the independent variable DISTANCE

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.655580424
R Square	0.429785693
Adjusted R Square	0.409420896
Standard Error	46.31938726
Observations	30
ANOVA
	df	SS	MS	F	Significance F
Regression	1	45279.06885	45279.07	21.10434	8.41E-05
Residual	28	60073.59782	2145.486
Total	29	105352.6667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	147.0811519	15.85028644	9.2794	4.88E-10	114.6133	179.5489914
Distrance	0.052650692	0.011460885	4.593947	8.41E-05	0.029174	0.07612725