Question

ONLY ANSWER E,F,G !!!!!!!!!!!!!!!!!!!!

A research center is interested in investigating the height and age of children who are between 5 to 9 4. years old. In order to do this, a sample of 15 children is selected and the data are given below. heicht will increax Height (inches) a/As the age Age (in years) inuease h 47.3 7 48.8 8 ADTY OU 41.3 50.4 8 51 47.1 7 46.9 7 48 7 51.2 51.2 40.3 5 48.9 8 45.2 6 41.9 49.6 8 a. Develop a scatter chart with age as the independent variable. What does the scatter chart indicate about the relationship between the height and age of children? b. Use the data to develop an estimated regression equation that could be used to estimate the height based on the age. What is the estimated regression model? c.How much of the variation in the sample values of height does the model estimated in part (b) explain? d.What is the predicted value of Y (height in inches) for a 6-year old? Develop 95% confidence interval for the predicted value. e. Interpretation of Standard Error for this problem. f. State the hypothesis for the Significance F and test the hypothesis. g.State the hypothesis for the significance of the independent variable and test the hypothesis

Answer 1

e)

The standard error of the regression (S) represents the average distance that the observed values fall from the regression line

f)

Ho: regression model is not significant

H1: regression model is significant

Regression Statistics
Multiple R	0.9696
R Square	0.9402
Adjusted R Square	0.9356
Standard Error	0.9179
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	172.1	172.1	204.27	0.0000
Residual	13	11.0	0.8
Total	14	183.1
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%
Intercept	27.9140	1.3751	20.2996	0.0000	24.9432	30.8847
X	2.7395	0.1917	14.2924	0.0000	2.3254	3.1536

F value = 204.27

p value=0.0000<α=0.05, reject Ho

so, regression model is sigificant

g)

Ho:   ß1=   0          
H1:   ß1╪   0          
n=   15              
alpha =   0.05              
estimated std error of slope =Se(ß1) = Se/√Sxx =    0.918   /√   22.93   =   0.1917
                  
t stat = estimated slope/std error =ß1 /Se(ß1) =    2.7395   /   0.1917   =   14.2924
                  
Degree of freedom ,df = n-2=   13              
p-value =    0.0000              
decison :    p-value<α , reject Ho              
Conclusion:   Reject Ho and conclude that slope is significantly different from zero