Question

1. A research center is interested in investigating the height and age of children who are between 5 to 9 years old. Please show the process of Excel analysis, thank you

In order to do this, a sample of 15 children is selected and the data are given below.

Age (in years)	Height (inches)
7	47.3
8	48.8
5	41.3
8	50.4
8	51
7	47.1
7	46.9
7	48
9	51.2
8	51.2
5	40.3
8	48.9
6	45.2
5	41.9
8	49.6

1. 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?

2. 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? (Note: You can use Excel to calculate)

1. Calculate SSR and SST (show your work, calculate by hand/excel math).

2. How much of the variation in the sample values of height does the model estimated in part (b) explain?

Answer 1

ANSWER

x	y
7	47.3
8	48.8
5	41.3
8	50.4
8	51
7	47.1
7	46.9
7	48
9	51.2
8	51.2
5	40.3
8	48.9
6	45.2
5	41.9
8	49.6

a)

This shows that there is positive linear relation

b)

Using Excel

data -> data analysis -> regression

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.96962237
R Square	0.940167541
Adjusted R Square	0.935565044
Standard Error	0.917919402
Observations	15
ANOVA
	df	SS	MS	F	Significance F
Regression	1	172.115845	172.115845	204.2733701	2.50199E-09
Residual	13	10.95348837	0.842576029
Total	14	183.0693333
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	27.9140	1.3751	20.2996	0.0000	24.9432
x	2.7395	0.1917	14.2924	0.0000	2.3254

y^ = 27.914 + 2.7395* x

d)

R^2 = 0.9402

hence 94.02 %

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