QuestionThe line of best fit is $\hat{y}=142.2 x-11,156$ . This line shows the comparison of house size in comparison to the cost of the house. If the size of the house, 1,800 square feet, gives the cost of $\$ 250,000$ , what is the $\hat{y}$ value given the line of best fit? (1 point) \ $250,000 \$244,804 \$267,116$ \ $2,855,489,760$

Studdy Solution

STEP 1

1. The line of best fit is given by the equation $\hat{y} = 142.2x - 11,156$ .
2. The variable $x$ represents the size of the house in square feet.
3. The variable $\hat{y}$ represents the predicted cost of the house.
4. We need to find the predicted cost $\hat{y}$ for a house size of 1,800 square feet.

STEP 2

1. Substitute the given house size into the line of best fit equation.
2. Calculate the predicted cost $\hat{y}$ .
3. Compare the calculated $\hat{y}$ with the given options.

STEP 3

Substitute $x = 1800$ into the equation $\hat{y} = 142.2x - 11,156$ :
$\hat{y} = 142.2(1800) - 11,156$

STEP 4

Calculate the value of $\hat{y}$ :
First, calculate $142.2 \times 1800$ :
$142.2 \times 1800 = 255,960$
Next, subtract 11,156 from 255,960:
$255,960 - 11,156 = 244,804$

STEP 5

Compare the calculated $\hat{y}$ value with the given options:
The calculated $\hat{y}$ value is \$244,804.
Therefore, the correct answer is:
$\boxed{244,804}$

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