Question
Use the least squares regression line of this data set to predict a value. Joseph is a crime scene investigator. He found a footprint at the site of a recent murder and believes the footprint belongs to the culprit. To help identify possible suspects, he is investigating the relationship between a person's height and the length of his or her footprint. He consulted his agency's database and found cases in which detectives had recorded the length of people's footprints, x, and their heights (in centimeters), y. Footprint length (in centimeters) Height (in centimeters) 24.01 169 24.92 175 28.33 172 28.68 184 29.85 189 The least squares regression line of this data set is: y=2.582x+107.679 How tall does this line predict someone should be if his or her footprint is 28.64 centimeters long? Round your answer to the nearest thousandth. centimeters
Answers
Answered by
GPT-4o mini
To predict the height using the least squares regression line equation \( y = 2.582x + 107.679 \), you can substitute the footprint length \( x = 28.64 \) into the equation.
Calculating:
\[
y = 2.582(28.64) + 107.679
\]
First, calculate \( 2.582 \times 28.64 \):
\[
2.582 \times 28.64 \approx 73.88528
\]
Now add \( 107.679 \):
\[
y \approx 73.88528 + 107.679 \approx 181.56428
\]
Rounding this value to the nearest thousandth gives:
\[
y \approx 181.564
\]
Thus, the predicted height for someone with a footprint length of 28.64 centimeters is **181.564 centimeters**.
Calculating:
\[
y = 2.582(28.64) + 107.679
\]
First, calculate \( 2.582 \times 28.64 \):
\[
2.582 \times 28.64 \approx 73.88528
\]
Now add \( 107.679 \):
\[
y \approx 73.88528 + 107.679 \approx 181.56428
\]
Rounding this value to the nearest thousandth gives:
\[
y \approx 181.564
\]
Thus, the predicted height for someone with a footprint length of 28.64 centimeters is **181.564 centimeters**.