Question

Using the same data, Complete the following a) Perform a linear regression analysis with height the independent variable and weight the dependent, i.e. weight = 0 + 1 × height + E

Using the same data, Complete the following a) Perform a linear regression analysis with height the independent variable and weight the dependent, i.e. weight = Bo + B1 x height +e • What is the prediction line equation? • What is the RP value for this regression? • What is the F-statistic value for testing the regressions significance? b) Test the hypotheses H:B1 = 0 vs He:B1 +0. • What is the standard error of bı? • what is the test statistic value for this hypothesis test? • What is the p-value for this test statistic? • Do you reject H.? c) Run two regressions, one for men and one for women. • What are the prediction line equations? • What are the R2 values for these regressions? d) Does the first regression for the entire data explain more of the variation than the later two? present evidence to support your answer.

Gender	Height	Weight
Male	73.84701702	241.8935632
Male	68.78190405	162.3104725
Male	74.11010539	212.7408556
Male	71.7309784	220.0424703
Male	69.88179586	206.3498006
Male	67.25301569	152.2121558
Male	68.78508125	183.9278886
Male	68.34851551	167.9711105
Male	67.01894966	175.9294404
Male	63.45649398	156.3996764
Male	71.19538228	186.6049256
Male	71.64080512	213.7411695
Male	64.76632913	167.1274611
Male	69.2830701	189.4461814
Male	69.24373223	186.434168
Male	67.6456197	172.1869301
Male	72.41831663	196.0285063
Male	63.97432572	172.8834702
Male	69.6400599	185.9839576
Male	67.93600485	182.426648
Male	67.91505019	174.1159291
Male	69.43943987	197.7314216
Male	66.14913196	149.173566
Male	75.20597361	228.7617806
Male	67.89319634	162.0066518
Male	68.1440328	192.3439766
Male	69.08963143	184.4351744
Male	72.80084352	206.8281894
Male	67.42124228	175.2139224
Male	68.49641536	154.3426389
Male	68.61811055	187.5068432
Male	74.03380762	212.9102253
Male	71.52821604	195.0322432
Male	69.1801611	205.1836213
Male	69.57720237	204.1641255
Male	70.40092889	192.9035151
Male	69.07617117	197.4882426
Male	67.19352328	183.8109732
Male	65.80731565	163.8518249

Answer 1

Answer:

Male data only given. Regression performed for male data only.

Excel Addon Megastat used.

Menu used: correlation/Regression ---- Regression Analysis.

a).

Regression Analysis
	r²	0.6705	n	39
	r	0.8188	k	1
	Std. Error of Estimate	12.5888	Dep. Var.	Weight
Regression output						confidence interval
variables		coefficients	std. error	t (df=37)	p-value	95% lower	95% upper
Intercept	a =	-265.0053	52.152	-5.081	0.0000	-370.674	-159.336
Height	b =	6.5343	0.753	8.677	0.0000	5.009	8.060
ANOVA table
Source	SS	df	MS	F	p-value
Regression	11,932.582	1	11,932.582	75.30	0.0000
Residual	5,863.636	37	158.477
Total	17,796.218	38

Prediction equation: weight = -265.0053+6.5343*height

R square =0.6705

F statistic = 75.30

b).

standard error of b1 = 0.753

test statistic = 8.677

yes, we reject Ho.

Height is significantly related to weight. 67.05% of variance in weight is explained by height.