Department of Education was analysing the average mathematics test score in the schools in Victoria. It noticed that there were dramatic differences in scores among the schools. In the attempt to improve the scores of all the schools, department attempted to determine the factors that account for the differences. Accordingly, they took a random sample of 40 schools across the state and for each determined the mean test score last year, the percentage of teachers in the schools who have at least one university degree in mathematics, the mean age and the mean annual income of the mathematics teachers.The following is regression output from Excel. SUMMARY OUTPUT Regression Statistics Multiple R0.597512 R Square0.357021 Adjusted R Square0.303439 Standard Error7.724526 Observations40 ANOVA dfSSMSFSignificance FRegression31192.732397.57746.6631250.001076925Residual362148.05959.6683 Total393340.791 CoefficientsStandard Errort StatP-valueLower 95%Intercept35.677627.2788494.9015472.03E-0520.91542769Math-DegreeA0.0698463.5432630.0011150.105828013AgeB0.1852131.3218860.194545-0.130798844Income ('000)C0.1528190.8722530.388851-0.176634459 You are required to;Derive the regression modelAssess the independent variables significance at 5% level (develop hypothesis if necessary in the analysis)?Discuss minimum of 3 assumption in OLS regression.

1. Regression model: From the output, t statMath-Degree=AStandard Error…

Answered: Department of Education was analysing…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

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Department of Education was analysing the average mathematics test score in the schools in Victoria. It noticed that there were dramatic differences in scores among the schools. In the attempt to improve the scores of all the schools, department attempted to determine the factors that account for the differences. Accordingly, they took a random sample of 40 schools across the state and for each determined the mean test score last year, the percentage of teachers in the schools who have at least one university degree in mathematics, the mean age and the mean annual income of the mathematics teachers.

The following is regression output from Excel.


SUMMARY OUTPUT

Regression Statistics
Multiple R	0.597512
R Square	0.357021
Adjusted R Square	0.303439
Standard Error	7.724526
Observations	40

ANOVA
	df	SS	MS	F	Significance F
Regression	3	1192.732	397.5774	6.663125	0.001076925
Residual	36	2148.059	59.6683
Total	39	3340.791

	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	35.67762	7.278849	4.901547	2.03E-05	20.91542769
Math-Degree	A	0.069846	3.543263	0.001115	0.105828013
Age	B	0.185213	1.321886	0.194545	-0.130798844
Income ('000)	C	0.152819	0.872253	0.388851	-0.176634459

You are required to;

Derive the regression model
Assess the independent variables significance at 5% level (develop hypothesis if necessary in the analysis)?
Discuss minimum of 3 assumption in OLS regression.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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