# Statistical Methods-Regression [ISS (Statistical Services) 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

### Describe in Detail

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

We first suppose the linear function of prediction is a + bX. Then the mean square error is given by

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## Question number: 2

» Statistical Methods » Regression » Polynomial

Appeared in Year: 2013

### Describe in Detail

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

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

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

The correlation coefficient is def

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## Question number: 3

» Statistical Methods » Regression » Linear

Appeared in Year: 2011

### Describe in Detail

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

Obtain the estimated linear regression of X on Y.

### Explanation

Let the linear equation is

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

To differential this, we get the estimate of and

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## Question number: 4

» Statistical Methods » Regression » Linear

Appeared in Year: 2015

### Describe in Detail

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

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

Can be tested by the statistic is

where is the standard error of an estimator b _{0}.

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