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

Equation

We first suppose the linear function of prediction is a + bX. Then the mean square error… (119 more words) …

Question number: 2

» Statistical Methods » Regression » Polynomial

Appeared in Year: 2013

Essay Question▾

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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

Equation

Equation

We know that the mean value of the given series satisfies the regression line that is Equation

Equation

The means of X and Y is calculate by multiply equation (1) by 2 to subtract equation (2), we get

Equation

Equation

The correlation coefficient is defined by… (40 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:

Equation

Obtain the estimated linear regression of X on Y.

Explanation

Let the linear equation is

Equation

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

Equation

To differential this, we get the estimate of Equation and Equation

Equation

Equation

The given… (24 more words) …

Question number: 4

» Statistical Methods » Regression » Linear

Appeared in Year: 2015

Essay Question▾

Describe in Detail

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

Equation

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

Equation

Can be tested by the statistic is

Equation

where Equation is the standard error of an estimator b 0.

Equation

Equation

where

Equation<span class="more">… (32 more words) …</span>

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