Question

Use the least squares regression line of this data set to predict a value.
Raymond and Wanda are judges for the Greenpoint Ice Staking Federation. Due to claims of malfeasance at recent competitions, a reporter is investigating the relationship between the scores awarded by the two judges.
She has collected the scores awarded by Raymond, x, and Wanda, y, for each performance in the last competition.
Raymond's score Wanda's score
0.45 2.55
1.10 1.71
1.83 3.02
3.15 2.90
3.58 2.80
4.42 3.67
The least squares regression line of this data set is:
y=0.305x+2.036
What score does this line predict Wanda would award a competitor to whom Raymond awards 2.81 points?
Round your answer to the nearest thousandth.
points

Answer 1

To predict the score Wanda would award using the least squares regression line, we can substitute Raymond's score (x = 2.81) into the regression equation:

\[
y = 0.305x + 2.036
\]

Now, substituting \(x = 2.81\):

\[
y = 0.305(2.81) + 2.036
\]

Calculating \(0.305 \times 2.81\):

\[
0.305 \times 2.81 = 0.85855
\]

Now, adding this to 2.036:

\[
y = 0.85855 + 2.036 = 2.89455
\]

Rounding to the nearest thousandth:

\[
y \approx 2.895
\]

Therefore, the predicted score that Wanda would award is **2.895 points**.