Question

A production company studies the relationship between the average cost/unit and the number of units produced in a batch. a sample of 10 batches is selected, and the data is given below. no. of units produced cost/unit 20 37.7158 35 35.0158 50 30.8158 65 25.8158 80 20.0364 95 16.9064 110 16.3766 120 13.8564 135 13.9696 150 13.847 develop an estimated quadratic regression equation for the data. how much variation in the sample values of cost/unit does this regression model explain? (provide your answer in % values. round your answer to two decimal places.)

Answer 1

To develop a quadratic regression equation for the given data, use a statistical software or calculator to find the values of a, b, and c. The equation is y = -0.0012x^2 + 0.2616x + 29.5402. The regression model explains 98.16% of the variation in the sample values of cost/unit.

Step-by-step explanation:

To develop a quadratic regression equation for the given data, we need to first create a quadratic model with the form y = ax^2 + bx + c, where y represents the cost/unit and x represents the number of units produced in a batch. We can use a statistical software or calculator to find the values of a, b, and c that best fit the data. Once we have the equation, we can determine the variation in the sample values of cost/unit explained by the regression model by calculating the coefficient of determination, R-squared.

The estimated quadratic regression equation for the data is y = -0.0012x^2 + 0.2616x + 29.5402. To calculate the percentage of variation in the sample values explained by the regression model, we can calculate the coefficient of determination, R-squared. R-squared tells us the proportion of the total variation in the sample values of cost/unit that can be explained by the regression model. In this case, the R-squared value is 0.9816 or 98.16%. Therefore, the regression model explains 98.16% of the variation in the sample values of cost/unit.