Math  /  Data & Statistics

Question4. The scatter plot represents the average yards gained xx and the average points scored per game yy in one season for ten randomly selected football teams. The equation of the line of best fit for this data is y=10.283+0.098xy=-10.283+0.098 x.
Football Team Statistics
Part A Complete the table by writing the unknown residual values. Round to the nearest tenth. \begin{tabular}{c|c|c} \begin{tabular}{c} Average Yards \\ Gained \end{tabular} & \begin{tabular}{c} Average Points \\ Scored \end{tabular} & Residual \\ \hline 247 & 15 & 1.1 \\ \hline 293 & 18 & 0.9 \\ \hline 300 & 20 & -1.5 \\ \hline 345 & 22 & -1.1 \\ \hline 361 & 24 & -0.2 \\ \hline 372 & 26 & \\ \hline \end{tabular}

Studdy Solution

STEP 1

What is this asking? We need to find the missing residual value for a football team that gained an average of 372 yards and scored an average of 26 points per game, given a line of best fit. Watch out! Remember, a residual is the *actual* value minus the *predicted* value.
Don't mix those up!

STEP 2

1. Calculate the predicted points.
2. Calculate the residual.

STEP 3

Alright, let's **predict** the average points scored using the line of best fit!
Our equation is y=10.283+0.098xy = -10.283 + 0.098x, where xx is the average yards gained.
We're given that the average yards gained is x=372x = 372.

STEP 4

Let's plug in x=372x = 372 into our equation: y=10.283+0.098372y = -10.283 + 0.098 \cdot 372.

STEP 5

Multiplying 0.0980.098 by 372372 gives us 36.45636.456.
So, y=10.283+36.456y = -10.283 + 36.456.

STEP 6

Adding 10.283-10.283 to 36.45636.456 gives us y=26.173y = 26.173.
This is our **predicted** average points scored.

STEP 7

Remember, the residual is the **actual** value minus the **predicted** value.
The **actual** average points scored is 2626, and we just calculated the **predicted** value to be 26.17326.173.

STEP 8

So, the residual is 2626.173=0.17326 - 26.173 = -0.173.

STEP 9

The problem asks us to round to the nearest tenth.
Rounding 0.173-0.173 to the nearest tenth gives us 0.2-0.2.
This is our **final residual**!

STEP 10

The residual for the team with 372 average yards gained and 26 average points scored is 0.2-0.2.

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