Question

Consider the x, y data:

x-data (explanatory variables):

10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65, 70, 75, 80, 85, 90, 95, 100

y-data (response variables):

1359.9265, 1353.3046, 220.7435, 964.6208, 1861.9920, 1195.3707, 1702.0145, 2002.0900, 1129.1860, 1864.5241, 1444.2239, 2342.5453, 2410.9056, 2766.2245, 2135.2241, 3113.7662, 4311.7260, 3313.1042, 4072.0945

Compute a best fit line to the data. Report:
a. The slope coefficient, β₁: ___

b. The intercept coefficient, β₀: ___

c. The standard error of the residuals σ_ε: ___

d. The Adjusted R-squared correlation coefficient Adjusted R²: ___

e. Is the slope coefficient significant at, at least the 95% level of confidence?

no

yes    

f. Is the intercept coefficient significant at, at least the 95% level of confidence?

yes

no    

Answer 1

using regression analysis from excel we get the following output shown here for the data given in question,

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.859509051
R Square	0.738755808
Adjusted R Square	0.723388503
Standard Error	558.141958
Observations	19
ANOVA
	df	SS	MS	F	Significance F
Regression	1	14975886.13	14975886	48.07321704	2.41661E-06
Residual	17	5295881.57	311522.4
Total	18	20271767.7
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%
Intercept	299.2933189	287.2736004	1.041841	0.312076215	-306.8009982	905.3876361	-306.8009982
X Variable 1	32.41819516	4.67559881	6.933485	2.41661E-06	22.55354395	42.28284636	22.55354395

form out put of excel

ANS

a)

32.4181951578947

b)

299.29331

c)

558.141958

d)

0.723388503

we are allowed to solve four sub parts only thank you