A quadratic regression model for data in the table below would be уhat = 0.0006x² + 0.958x - 37
The coefficient of determination, r² = 0.9287
What is the quadratic regression model?
The quadratic regression model is given by the general formula;
y = ax² + bx + c
where:
y is the dependent variable
x is the independent variable
a, b, c are the coefficients of the model
This is exemplified in the equation;
уhat = 0.0006x² + 0.958x - 37
a = 0.006, b = 0.9588, c = -37
The coefficient of determination obtained with the spreadsheet formula
= RSQ(A1:A4, B1;B4)
= 0.9287
With the above regression model, the table can be completed as follows;
x y yhat y - yhat
50 15 9.4 5.6
100 36 52.8 -16.8
150 110 93.2 16.8
200 125 130.6 -5.6
Complete Question:
5. A local print shop sells yard signs for realtors in bundles of 50 signs. The profit margins for each bundle are shown below. Assume the behavior is a quadratic regression for a up to 800 signs.
A. Find a quadratic regression model for data in the table below. Use the model to complete the table. _ Quadratic Regression Model:
B. Record the coefficient of determination, r^2.