Question

The following data is used to study the relationship between miles traveled and ticket price for a commercial airline:

Distance in miles:        300      400      450      500      550      600      800      1000

Price charged in $:      140      220      230      250      255      288      350      480

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.987
R Square	0.975
Adjusted R Square	0.971
Standard Error	17.352
Observations	8
ANOVA
	df	SS		MS	F	Significance F
Regression	1	70291.3		70291.3	233.4	4.96363E-06
Residual	6	1806.6		301.1
Total	7	72097.9
	Coefficients	Standard Error		t Stat	P-value
Intercept	22.547	17.725		1.272	0.250
Distance in miles:	0.442	0.029		15.279	4.96E-06

What is the slope of the least squares line?

22.547

0.975

0.442

17.352

About what percentage of the variation in Price Charged is explained by its regression on the distance in miles?

0.442

22.547

17.352

97.5

Based on the outcome of the hypothesis test for the slope of the regression line at the 5% significance level, we can conclude that:

a) There is sufficient evidence that Distance causes Price.

b) There is insufficient evidence that there is a relationship between Distance and Price.

c) There is sufficient evidence that the slope of the regression line is positive.

d) There is sufficient evidence that the slope of the regression line is not zero. This model is statistically significant.

Answer 1

Q1) From the coefficients column, we can see here that the coefficient for the variable: Distance in Miles here is given as 0.442. Therefore the slope of the least square line here is given as: 0.442.

Q2) The coefficient of determination here is given as: R² = 0.975

Therefore, 97.5% of the variation in the the dependent variable is explained by the variation in the independent variable that is explained by regression here.

Q3) From the coefficient table, we have the p-value for the slope coefficient here as: 4.96 x 10^-6. As this p-value is very very low here, therefore the test is significant here. Therefore there is sufficient evidence that the slope of the regression line is not zero .Therefore d) is the correct answer here.

The model is significant here.