Question

The Northwestern Railroad Company is interested in analyzing how fuel consumption is associated to the number of railcars its trains use on certain routes between Dallas and Chicago. A random sample of ten trains on this particular route has yielded the following data displayed below (the number of railcars represents the independent variable and fuel consumption represents the dependent variable):

#of railcars fuel consumption(units/mile)

20 58

20 52

37 91

31 100

47 114

43 98

39 87

50 122

40 100

29 70

The regression equation is

Predictor Coefficient Standard Deviation T-test P-value

Constant 16.103 5.157 3.12 0.072

Railcar 2.0553 0.1396 14.72 0.000

S=4.361 R-Sq+87.1% R-Sq(adj)=96.3%

6. Is a linear model appropriate for modeling this data? Clearly explain your reasoning by typing or writing legible for your answer.

Answer 1

Regression equation: y = 16.103 + 2.0553x

6. Correlation coefficient (r) = 0.871^0.5 = 0.933

n = 10, Degrees of freedom: df = n-2 = 8, Level of significance = 0.05

H₀: ρ = 0, A linear model is not appropriate for modeling the data

H₁: ρ ≠ 0, A linear model is appropriate for modeling the data

Test statistic = r*((1-r*r)/(n-2))^0.5 = 0.933*((1-0.933*0.933)/(10-2))^0.5 = 0.119

Critical value (Using Excel function T.INV.2T(probability,df)) = T.INV.2T(0.05,8) = 2.306

Since test statistic is less than critical value, we do not reject the null hypothesis and conclude that ρ = 0.

So, a linear model is not appropriate for modeling the data.