Question

You are estimating the cost of optical sensors based on the resolution of the sensor. You decide to calculate the coefficient of determination (R2) as part of determining the goodness of fit of an equation. Using the preliminary calculations below, calculate the R2 and determine its meaning.

Summation of (Yi - Ybar)2 = 147172
Summation of (Yhat - Ybar)2 = 130542
Summation of (Y - Yhat)2 = 16630
a. 88.70% of the variation in the cost is being explained by the resolution.
b. 88.70% of the variation in the resolution is being explained by the cost.
c. 11.30% of the variation in the resolution is being explained by the cost.
d. 11.30% of the variation in the cost is being explained by the resolution.

Answer 1

a. 88.70% of the variation in the cost is being explained by the resolution.

Explanation:

Given :

Summation of (Yi - Ybar)2 = 147172

Summation of (Yhat - Ybar)2 = 130542

Summation of (Y - Yhat)2 = 16630

The Coefficient of determination (R²) :

Sum of Square regression (SSR) / sum of square TOTAL (SST). It gives the percentage of the dependent variable which can be explained by the regression line.

Cost is the dependent variable in this scenario.

SSR = Summation of (Yhat - Ybar)2 = 130542

SST = Summation of (Yi - Ybar)2 = 147172

Hence,

SSR / SST = 130542 / 147172

R² = 130542 / 147172

R² = 0.8870029 = (0.8870029 * 100%) = 88.7%