IGNOU MTE 3 2018 - An economist wants to estimate the relationship between a family&rsquo

Question

An economist wants to estimate the relationship between a family’s annual income and the amount that the family saves. The family data for nine families are obtained

Annual income (thousands of Rs.)	12	13	14	15	16	17	18	19	20
Annual saving (thousands of Rs.)	0.0	0.1	0.2	0.2	0.5	0.5	0.6	0.7	0.8

Calculate the least square regression line where annual savings is the dependent variable and annual income is the independent variable.

02 Feb 2018

Answer :

Word Count : 508

To calculate the least squares regression line, we need to find the equation of the form: \[ y = \beta_0 + \beta_1 x \] where: - \( y \) is the dependent variable (annual savings), - \( x \) is the independent variable (annual income), - \( \beta_0 \) is the intercept, and - \( \beta_1 \) is the slope of the regression line. ### Step 1: Calculate the necessary sums The formulas for the slope \( \beta_1 \) and the intercept \( \beta_0 \) are: \[ \beta_1 = \frac{n \sum{x y} - \sum{x} \sum{y}}{n \sum{x^2} - (\sum{x})^2} \] \[ \beta_0 = \frac{\sum{y} - \beta_1 \sum{x}}{n} \] Where \( n \) is the number of data points. We will calculate the following

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