Question

A firm wants to know whether there is any linear relationship between the sales (X) and its yearly revenue (Y). The records for 10 years were examined and the following results were obtained:

equation

(a) Fit a regression line taking Y as the dependent variable and X as the independent variable.

(b) Test whether the sales have any effect on revenue at 5% level of significance. (c) Comment on the goodness of fit of the regression line.

20 Feb 2025
Answer :
Word Count : 575

(a) Fit a regression line taking Y as the dependent variable and X as the independent variable.

To fit a regression line, we will use the formula:

\[
Y = \beta_0 + \beta_1 X
\]

Where:
- \( Y \) is the dependent variable (yearly revenue),
- \( X \) is the independent variable (sales),
- \( \beta_0 \) is the intercept,
- \( \beta_1 \) is the slope.

The coefficients can be calculated using the following formulas:

\[
\beta_1 = \frac{n \sum XY - (\sum X)(\sum Y)}{n \sum X^2 - (\sum X)^2}
\]
\[
\beta_0 = \frac{\sum Y - \beta_1 \sum X}{n}
\]

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