Question

Develop a 95% confidence interval estimate that the higher the price of the car, the higher the road test scores using Excel.

Price ($)
23,970.00
21,885.00
23,830.00
32,360.00
23,730.00
22,035.00
21,800.00
23,625.00
24,115.00
29,050.00
28,400.00
30,335.00
28,090.00
28,695.00
30,790.00
30,055.00
30,094.00
28,045.00
27,825.00
28,995.00

Road-Test Score
91
81
83
84
80
73
89
76
74
84
80
93
89
90
81
75
88
83
52
63

  

Answer 1

Regression Statistics
Multiple R	0.0488
R Square	0.0024
Adjusted R Square	-0.0530
Standard Error	10.1612
Observations	20
ANOVA
	df	SS	MS	F	Significance F
Regression	1	4.44	4.44	0.04	0.8381
Residual	18	1858.51	103.25
Total	19	1862.95
	Coefficients	Standard Error	t Stat	P-value	lower 95%	upper 95%
Intercept	76.6002	18.713	4.093	0.0007	37.2857	115.91
price	0.0001	0.001	0.207	0.5809	-0.0013	0.0016

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confidence interval for slope                  
α=   0.05              
t critical value=   t α/2 =    2.101   [excel function: =t.inv.2t(α/2,df) ]      
estimated std error of slope = Se/√Sxx =    10.16124   /√   216330077.20   =   0.001
                  
margin of error ,E= t*std error =    2.101   *   0.001   =   0.001
estimated slope , ß^ =    0.0001              
                  
                  
lower confidence limit = estimated slope - margin of error =   0.0001   -   0.001   =   -0.0013
upper confidence limit=estimated slope + margin of error =   0.0001   +   0.001   =   0.0016