You are estimating the cost of optical sensors based on the radius of the sensor

Question

You are estimating the cost of optical sensors based on the radius of the sensors. 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.

[Image Description: Summation of (Yi – Ybar)2 = 147172 Summation of (Yhat – Ybar)2 = 129217 Summation of (Y– Yhat))2 = 17955]    12.20% of the variation in the cost is being explained by the radius.    87.80% of the variation in the radius is being explained by the cost.    87.80% of the variation in the cost is being explained by the radius.    12.20% of the variation in the radius is being explained by the cost. You are estimating the cost of optical sensors based on the radius of the sensors. 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.

[Image Description: Summation of (Yi – Ybar)2 = 147172 Summation of (Yhat – Ybar)2 = 129217 Summation of (Y– Yhat))2 = 17955]    12.20% of the variation in the cost is being explained by the radius.    87.80% of the variation in the radius is being explained by the cost.    87.80% of the variation in the cost is being explained by the radius.    12.20% of the variation in the radius is being explained by the cost.

Explanation / Answer

Answer: R^2 is calculated as regression sums of squares / total sums of squares. Thus,
R^2 = 17955/147172 = 12.20%
Our model is trying to explain the cost of optical sensors, so the answer is:
(A) 12.20% of the variation in the cost is being explained by the radius.

Related Questions

Navigate

• Browse (All)
• Browse Y
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.