Match the items of List - I with the items of List - II and indicate the code of their correct matching with regard to correlation and regression analysis : CodesList - I List - II a. $\gamma_{xy} \frac{\sigma_y}{\sigma_x}$ i. Covariance between X and Y b. $\frac{\Sigma(X - \bar{X}) (Y - \bar{Y})}{n \cdot \sigma_x \cdot \sigma_y}$ ii. Standard error of coefficient of correlation c. $\frac{\Sigma(X - \bar{X}) (Y - \bar{Y})}{n}$ iii. Regression coefficient of Y on X variable d. $\frac{1 - \gamma^2}{\sqrt{n}}$ iv. Karl Pearson's coefficient of correlation
Matching Correlation and Regression Concepts
This question requires matching statistical terms and formulas related to correlation and regression analysis from List - I to List - II.
List - I Item Analysis:
- a. $\gamma_{xy} \frac{\sigma_y}{\sigma_x}$: This formula represents the Regression coefficient of Y on X. It's denoted as $b_{yx}$.
- b. $\frac{\Sigma(X - \bar{X}) (Y - \bar{Y})}{n \cdot \sigma_x \cdot \sigma_y}$: This is the definition of Karl Pearson's coefficient of correlation ($\gamma$ or $r$), which standardizes the covariance by the product of standard deviations.
- c. $\frac{\Sigma(X - \bar{X}) (Y - \bar{Y})}{n}$: This formula calculates the sample Covariance between X and Y ($\text{Cov}(X,Y)$).
- d. $\frac{1 - \gamma^2}{\sqrt{n}}$: This formula approximates the Standard error of the coefficient of correlation ($SE_r$) for large sample sizes.
Matching Summary:
- a matches with iii (Regression coefficient of Y on X)
- b matches with iv (Karl Pearson's coefficient of correlation)
- c matches with i (Covariance between X and Y)
- d matches with ii (Standard error of coefficient of correlation)
The correct matching code is therefore a-iii, b-iv, c-i, d-ii.
Important Questions from Correlation and Regression
If r is the coefficient of correlation between x and y, then what is the correlation coefficient between (3x + 4) and (-3y + 3)?
Which of the following statements is/are correct in respect of regression coefficients?
1. It measures the degree of linear relationship between two variables
2. It gives the value by which one variable changes for a unit change in the other variable.
Select the correct answer using the code given below.If two lines of regression are x + 4y + 1 = 0 and 4x + 9y + 7 = 0, then what is the value of x when y = -3 ?
A bivariate data set contains only two points (-1, 1) and (3, 2). What will be the line of regression of y on x ?
If two regression lines between height (x) and weight (y) are 4y – 15x + 410 = 0 and 30x – 2y – 825 = 0, then what will be the correlation coefficient between height and weight?
