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 
4.96363E06 

Residual 
6 
1806.6 
301.1 

Total 
7 
72097.9 

Coefficients 
Standard Error 
t Stat 
Pvalue 

Intercept 
22.547 
17.725 
1.272 
0.250 

Distance in miles: 
0.442 
0.029 
15.279 
4.96E06 
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.
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: R^{2} = 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 pvalue for the slope coefficient here as: 4.96 x 10^{6}. As this pvalue 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.
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