Answer to Question #113789 in Statistics and Probability for Attiya Fatima

Question

How can I make my statistical data on Ms word? And if the relation is indirect then how regression line touches to Y-axis?

Answer 1

(1) Get the data for the dependent and independent variable in column format.

(2) Type in the data, either in comma separated or space separated format.

x data (comma or space separated)

y data (comma or space separated)

The independent variable is x, and the dependent variable is y. In order to compute the regression coefficients, the following table needs to be used:

$$\begin{matrix} & x & y & xy & x^2 & y^2 \\ & x_2 & y_2 & x_2y_2 & x_2^2 & y_2^2 \\ & ... &... & ... & ... & ... \\ & x_n & y_n & x_ny_n & x_n^2 & y_n^2 \\ Sum= & \sum x_i & \sum y_i & \sum{ x_iy_i} &\sum{x_i^2} & \sum{y_i^2} \end{matrix}$$

Based on the above table, the following is calculated:

$$\bar{x}={1\over n}\displaystyle\sum_{i=1}^nx_i, \ \bar{y}=\displaystyle\sum_{i=1}^ny_i$$

$$SS_{xx}=\displaystyle\sum_{i=1}^nx_i^2-{1\over n}\bigg(\displaystyle\sum_{i=1}^nx_i\bigg)^2$$

$$SS_{yy}=\displaystyle\sum_{i=1}^ny_i^2-{1\over n}\bigg(\displaystyle\sum_{i=1}^ny_i\bigg)^2$$

$$SS_{xy}=\displaystyle\sum_{i=1}^nx_iy_i-{1\over n}\bigg(\displaystyle\sum_{i=1}^nx_i\bigg)\bigg(\displaystyle\sum_{i=1}^ny_i\bigg)$$

Therefore, based on the above calculations, the regression coefficients (the slope $m,$ and the y-intercept $n$) are obtained as follows:

$$m={S_{xy}\over S_{xx}}$$

$$n=\bar{y}-m\cdot\bar{x}$$

Therefore, we find that the regression equation is:

$$y=n+mx$$

The linear relationship between two variables is negative when one increases as the other decreases. For example, as values of x get larger values of y get smaller. This is also known as an indirect relationship.

$$y=n+mx, m<0$$

How regression line touches to Y-axis?

$$x=0: y=n$$

Point $(0, n)$