Math Snap

STEP 1

Assumptions1. The data given is accurate and reliable.
. A linear model is appropriate for these data.
3. The relationship between the amount of snow and the attendance is inversely proportional.

STEP 2

We first need to find the slope and y-intercept of the regression line. The formula for the slope (m) of the regression line is$$m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}$$where- n is the number of data points- $\sum xy$ is the sum of the product of x and y- $\sum x$ is the sum of x- $\sum y$ is the sum of y- $\sum x^2$ is the sum of the squares of x

STEP 3

We calculate the necessary sums for the slope formula. We have7 data points, so n=7. We calculate $\sum x$, $\sum y$, $\sum xy$, and $\sum x^2$ using the given data.

STEP 4

We calculate the slope (m) using the formula and the sums calculated in the previous step.

STEP 5

Now we need to find the y-intercept (b) of the regression line. The formula for the y-intercept is$$b = \frac{\sum y - m(\sum x)}{n}$$where- m is the slope- n is the number of data points- $\sum x$ is the sum of x- $\sum y$ is the sum of y

STEP 6

We calculate the y-intercept (b) using the formula and the sums and slope calculated in the previous steps.

STEP 7

Now we have the equation of the regression line in the form$$Attendance = m(\text{Inches of Snow}) + b$$where m is the slope and b is the y-intercept.

STEP 8

We use the equation of the regression line to predict the attendance at a concert when there are.1 inches of snow on the ground. We substitute.1 for Inches of Snow in the equation and calculate the result.

We round the result to the nearest integer to get the predicted attendance.