A company wants to estimate, how its monthly costs are related to its monthly output rate. The data for a sample of nine months is tabulated below :

Using the data given above, perform following tasks:

(a) Calculate the best linear regression, where the monthly output is the dependent variable and monthly cost is the independent variable.

(b) Use the regression line to predict the company’s monthly cost, if they decide to produce 4 tons per month.

To perform linear regression, we need to calculate the slope and intercept of the regression line using the given data. The formula for the slope (b) and intercept (a) in a simple linear regression is given by:

\[ b = \frac{N(\sum xy) - (\sum x)(\sum y)}{N(\sum x^2) - (\sum x)^2} \]

\[ a = \frac{(\sum y) - b(\sum x)}{N} \]

where:
- N is the number of data points,
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