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Correlation and Regression Questions and Answers

11.

In a multiple regression model, the f-ratio is used to test the

Exam Year(s)

UGC NET - 2012,

Answer: D

The f-ratio in a multiple regression model tests the overall goodness of fit of the model. It is the ratio of the mean square explained by the regression to the residual mean square, and it asks whether all the slope coefficients together could be zero. A large f-ratio means the predictors as a group explain a significant part of the variation. It does not test the variance of the data or the standard error of the mean, and R-squared is the measure of fit itself, while the f-ratio is the significance test built on it.

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12.

In a simple regression analysis of y on x, the standard error of estimate of y on x, \(S_{yx}\) = 5, number of observations N is 30, and \(\sum y^{2}\) = 2000. The unexplained variance is

Exam Year(s)

UGC NET - 2013,

Answer: B

The unexplained variation is the standard error of estimate squared multiplied by the number of observations.

\[ \sum (y - \hat{y})^2 = N \, S_{yx}^2 \]

\[ = 30 \times 25 = 750 \]

So the unexplained variance is 750, option B. The explained part is the remainder of the 2000.

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13.

The Pearson Linear correlation coefficient (r) for the following paired data (x, y) : (2, 1.4) (4, 1.8), (8, 2.1), (8, 2.3), (9, 2.6) is

Exam Year(s)

UGC NET - 2013,

Answer: C

The Pearson correlation is the covariance of x and y divided by the product of their spreads. The means are 6.2 for x and 2.04 for y.

\[ r = \frac{S_{xy}}{\sqrt{S_{xx} S_{yy}}} \]

\[ S_{xy} = \sum (x - \bar{x})(y - \bar{y}) \]

\[ r \approx 0.957 \]

So the answer is 0.957, option C. A negative value is impossible as y rises with x.

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