Operations Management - Regression Projects

QUANTITATIVE ANALYSIS II Questions II (to be handed in) The maximum volume of air that a person can breathe

QUANTITATIVE ANALYSIS II

Questions II (to be handed in)

The maximum volume of air that a person can breathe out in one second (FEV1: Forced expiratory volume in 1 second) is a measure of lung function used in respiratory disease (e.g., asthma). A study of lung function among 636 children aged 7 to 10 years living in a deprived suburb of Lima, Peru, was undertaken to explore the relationships between FEV1 and exposure variables such as age and height, and to determine if those relationships vary with gender. Below are tables of computer outputs for different regression models.

Question II.1 (20 points)

Table 1: ANOVA Table for the multiple linear regression relating FEV1 to age and height

Source of variations	Sum of Squares	df	MS	F	p-value < 0.0001
Regression	25.6383				p-value < 0.0001
Error
Total	58.8584	635

Table 2: Regression coefficients for the multiple linear regression relating FEV1 to age and height

Model		B	Std. Error	tobserved	p-value
1	Intercept	-2.3087	0.1812		p-value
	Age	0.0897	0.0157
	Height	0.0250	0.0018

Complete the ANOVA Table 1 and use the information in that table to decide if the linear relationship hypothesized is statistically significant. (10 points)
Utilizing the information from Table 1, compute the value of the coefficient of determination (R2),
and give a simple interpretation for the R ² value you calculated. (5 points)
Complete the regression parameter estimates Table 2 and test if the slope of the straight-line regression is significant. (5 points)

Question II.2 (15 points)

Table 3: Regression coefficients for the linear regression relating FEV1 to gender

Model		B	Std. Error	tobserved	p-value < 0.0001
1	Intercept	1.5384	0.0163	94.22	p-value < 0.0001
	Male	0.1189	0.0237	5.01	< 0.0001

Define the dummy variable for gender. (5 points) What is the difference in mean FEV1 between boys and girls? (5 points) Answer:
Are males and females significantly different on average in terms of their FEV1 levels? Write down hypotheses to be tested. Use á = 5% as the significance level. (5 points)

Question II.3 (15 points)

Table 4: Regression coefficients for the linear regression relating FEV1 to age, height and gender

Model		B	Std. Error	tobserved	p-value < 0.0001
1	Intercept	-2.360	0.1750	-13.49	p-value < 0.0001
	Age	0.0946	0.0152	6.23	< 0.0001
	Height	0.0246	0.0018	14.04	< 0.0001
	Male	0.1213	0.0176	6.90	< 0.0001

Did the adjustment for age and height change the difference between boys and girls? (5 points) .
Write down the regression equations (overall as well as for males and females). (5 points)
What is the expected FEV1 value for a child, male, 140 cm tall and 9.5 years old? (5 points)

Price: $6.86

Solution: The downloadable solution consists of 2 pages, 486 words and 4 charts.
Deliverable: Word Document