Question

Suppose that you are told that the weight of a vehicle in pounds (X) and the fuel consumption in miles per gallon(Y) are linearly related according to the model

$Y=\beta _{0}+\beta _{1}X+\epsilon$

Where $\epsilon$ represents the measurement error.

X	Y
3985	24
3225	27
2300	37
2500	34
2780	31

NOTE: The prediction equation is also, it is given that MSE=2.262 and

a). Predict the fuel consumption for a vehicle weighing 3000 pounds

b). Compute a 95% confidence interval for the fuel consumption for a vehicle weighing 3000 pounds.

c). Check whether the standard error for the slope estimate = 0.001121

d). Verify that the slope is indeed negative by using a hypothesis test at

in full details please!

Y - 52.9-0.00754X Σ(ri-X)2 = 180042724 a-0.05

Answer 1

(a) Predicted fuel consumption 52.9-0.00754 3000 30.28 gallons (b) to.o25,3 3.1824, X (3985 3225 23002500 +2780)/5 2958, Sr-Ž (Xi-X )-1 800427.24. MSF-2.262. 희-30.28 95% C.1. for fuel consumption for a vehicle weighing 3000 pounds : 1 (3000 X)2 (3000-X)2) 1 . (28.13 gallons, 32.43 gallons) MSE = 0.001121 (c) Standard error for the slope estimate-se(A)- (d) Null hypothesis. Ho : β1 =0 us. Alternative hypothesis. H1 : β1 < 0 where β-slope of true regression line 31 Value of t test-- 0.00754/0.001121 =ー6.7261 t se(Bi) where, β!--0.00754 p-value P(t <-6.7261|t ~ ts) = 0.0034 < 0.05 Hence we reject Ho at 5% level of significance and we can conclude that the slope is indeed negative