Statistical Methods-Regression (ISS Statistics Paper I (Old Subjective Pattern)): Questions 1 - 4 of 4

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Question number: 1

» Statistical Methods » Regression » Linear

Appeared in Year: 2011

Essay Question▾

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Show that the best predictor of Y, in terms of minimum MSE, is linear in X, if (X, Y) has bivariate normal distribution.

Explanation

We have two random variables X and Y. We use the value of X to predict Y and (X, Y) has bivariate normal distribution. The correlation coefficient is ρ=Corr (X, Y). Let

(X,Y)~BN(μX,μY,σX2… (416 more words) …

Question number: 2

» Statistical Methods » Regression » Polynomial

Appeared in Year: 2013

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Given the two regression lines between X and Y, 2Y -X - 50 = 0, 3Y-2X - 10 = 0, compute the means of X and Y and the correlation coefficient between X and Y.

Explanation

Given that

2YX50=0

3Y2X10=0

We know that the mean value of the given series satisfies the regression line that is 2YX=50.(1)

3… (130 more words) …

Question number: 3

» Statistical Methods » Regression » Linear

Appeared in Year: 2011

Essay Question▾

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From a bivariate data set of 4995 observations, the following quantities have been calculated:

x=2353,x2=9508,y=1400,y2=70802,xy=8805

Obtain the estimated linear regression of X on Y.

Explanation

Let the linear equation is

X=β0+β1Y+ε

To solve this equation by least square method. In this approach, the residual sum of squares is minimized by partially differentiating with respect to β0 and β1.

ε2=… (139 more words) …

Question number: 4

» Statistical Methods » Regression » Linear

Appeared in Year: 2015

Essay Question▾

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For 20 pairs of heights of father (X) and son (Y) measured in cm, the following data are obtained:

x=168.17,(xix)2=777.80,(yiy)2=989.42,y=9.25+0.932x

Test whether the cut on the X-axis can be assumed to be zero, at 5 % level of significance.

Explanation

In the regression model, the cut on the X-axis can be assumed to be zero means the intercept zero. The test of the hypothesis is

H0:β0=0vsH1:β00

Can be tested by the statistic is

t=… (199 more words) …

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