Question

Use the least squares regression line of this data set to predict a value.
Kiara wants to figure out how long it usually takes to get through a supermarket checkout line. For several weeks, she observed the checkout lines she waited in.
Kiara counted how many people were ahead of her in each line she joined, x, and how many minutes it took her to get to the front of that line, y.
People Minutes
1 2
2 6
4 15
6 13
7 13
The least squares regression line of this data set is:
y=1.808x+2.569
How long does this line predict Kiara would have to wait if there were 3 people ahead of her?
Round your answer to the nearest integer.
minutes

Answer 1

To predict how long Kiara would have to wait if there were 3 people ahead of her, we can use the least squares regression line equation:

\[ y = 1.808x + 2.569 \]

Here, \( x \) is the number of people ahead of her. Plugging in \( x = 3 \):

\[ y = 1.808(3) + 2.569 \]

Calculating the right side:

1. Calculate \( 1.808 \times 3 = 5.424 \)
2. Now, add \( 2.569 \) to \( 5.424 \):

\[ y = 5.424 + 2.569 = 7.993 \]

Rounding \( 7.993 \) to the nearest integer gives \( 8 \).

Thus, the prediction for how long Kiara would have to wait if there were 3 people ahead of her is **8 minutes**.