Question

LUIS SUUUU UC AUSWUCu. V. A planner postulates the slum occurrence in cities (y) can be explained by the age of the cities (xi) and the rate of in - migration into the cities (x). To test this postulation, the data below were obtained 9 10 14 14 Compute the multiple correction coefficient and explain what it means (i) (ii) Differentiate between parametric and non-parametric statistical test. Proceed to give one example of each (iii) Proceed to consider the advantages and disadvantages of secondary data.

a planner postulates the slum occurencies in cities (y) can be explained by the age of the cities (x1) and the rate of in-migration into the cities (X2)

Question
1. Compute the multiple correlation coefficient and explain what it means

Answer 1

Y	X1	X2	y=Y-MeanY	x1=X1-mean X1	x2=X2-meanX2	(Y-MeanY)^2	(X1-meanX1)^2	(X2-meanX2)^2	(Y-meanY)(X1-MeanX1)	(Y-meanY)(X2-MeanX2)	(X2-meanX2)(X1-MeanX1)
2	1	5	-4.25	-6.41667	-5.75	18.0625	41.17362	33.0625	27.27083	24.4375	36.89584
1	3	5	-5.25	-4.41667	-5.75	27.5625	19.50695	33.0625	23.1875	30.1875	25.39584
4	8	7	-2.25	0.583333	-3.75	5.0625	0.340277	14.0625	-1.3125	8.4375	-2.1875
3	4	10	-3.25	-3.41667	-0.75	10.5625	11.67361	0.5625	11.10417	2.4375	2.5625
5	4	11	-1.25	-3.41667	0.25	1.5625	11.67361	0.0625	4.270834	-0.3125	-0.85417
5	5	11	-1.25	-2.41667	0.25	1.5625	5.840279	0.0625	3.020834	-0.3125	-0.60417
7	10	12	0.75	2.583333	1.25	0.5625	6.673609	1.5625	1.9375	0.9375	3.229166
8	9	14	1.75	1.583333	3.25	3.0625	2.506943	10.5625	2.770833	5.6875	5.145832
10	8	14	3.75	0.583333	3.25	14.0625	0.340277	10.5625	2.187499	12.1875	1.895832
11	9	9	4.75	1.583333	-1.75	22.5625	2.506943	3.0625	7.520832	-8.3125	-2.77083
10	14	15	3.75	6.583333	4.25	14.0625	43.34027	18.0625	24.6875	15.9375	27.97917
9	14	16	2.75	6.583333	5.25	7.5625	43.34027	27.5625	18.10417	14.4375	34.5625
					total(sums)	126.25	188.9167	152.25	124.75	105.75	131.25

rxy = Σ(x; – X)(y - y) Σ(x; - X)? Σy; - y)2

this is the formula for simple correlation coefficient. here (Xi-X bar) means (Xi-mean of Xi) and so on

hence r_{y x1}=0.807774, r_{y x2}=0.762757, r_x1.x2= 0.773901 (put the sums of the table in the formula to get these values)

now the formulas for multiple correlations is
The formula for R is + ri; – 29.7x; ix• ';, '; 1- where ra, = correlation coefficient for y and xı Pa = correlation coefficient for y and x2 Prors = correlation coefficient for x, and x2

The formula for R is + ri; – 29.7x; ix• ';, '; 1- where ra, = correlation coefficient for y and xı Pa = correlation coefficient for y and x2 Prors = correlation coefficient for x, and x2

The formula for R is + - 21.:, "x %x; ^ V l-laky where r = correlation coefficient for y and xı rv = correlation coefficient for y and x2 rura = correlation coefficient for xy and x2

hence R=0.8364925

Interpretation:

The multiple correlation coefficient means how a change in the dependent variable(Y here) can be explained by the change in the independent variables(x1 and x2 here).the closer the value of R is to zero the better the explanatory power is.

in this case, it means, the occurrence of the slums can be explained by the age of the cities and the rate of migration very strongly as our value of R is almost 0.84.

2. solution:

A Parametric test assumes some statistical distributions(and the means and standard deviations) in the given data. Hence, a list of conditions of validity tests should be done so that the result of a parametric test is reliable. For e.g., Student’s t-test for two independent samples is reliable only when

a.each sample follows a normal distribution

b. sample variances are homogeneous.

Nonparametric tests do not rely on any distribution. They can thus be applied even if parametric conditions of validity are not met. for e.g chi square test.

iii. Answer:

advantages of secondary data:

1. Data is easily accessible in the websites and databases. hence low cost of data collection

2. the background for using the data is already validated before so that data can be used without doing much literature review.

Disadvantages of secondary data;

1.secondary data may get outdated or they may have some errors

2. they can be collected as primary data in some particular special cases, hence the usage of the data in a new study may be unreliable.

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