Question

Consider the following data on x = weight (pounds) and y = price ($) for 10 road-racing bikes.

Brand	Weight	Price ($)
A	17.8	2,100
B	16.1	6,150
C	14.9	8,370
D	15.9	6,200
E	17.2	4,000
F	13.1	8,600
G	16.2	6,000
H	17.1	2,480
I	17.6	3,300
J	14.1	8,000

These data provided the estimated regression equation  ŷ = 28,750 − 1,452x. For these data, SSE = 7,198,472.68 and SST = 53,025,800.Use the F test to determine whether the weight for a bike and the price are related at the 0.05 level of significance.

Find the value of the test statistic. (Round your answer to two decimal places.)

Answer 1

The statistic software output for this problem is :

Simple linear regression results:
Dependent Variable: Price ($)
Independent Variable: Weight
Price ($) = 28750.175 - 1451.8859 Weight
Sample size: 10
R (correlation coefficient) = -0.92964824
R-sq = 0.86424584
Estimate of error standard deviation: 948.58267

Parameter estimates:

Parameter	Estimate	Std. Err.	Alternative	DF	T-Stat	P-value
Intercept	28750.175	3268.9003	≠ 0	8	8.7950603	<0.0001
Slope	-1451.8859	203.44425	≠ 0	8	-7.1365297	<0.0001

Analysis of variance table for regression model:

Source	DF	SS	MS	F-stat	P-value
Model	1	45827327	45827327	50.930056	<0.0001
Error	8	7198472.7	899809.08
Total	9	53025800

The value of the test statistic = 50.93