Math Snap

STEP 1

Assumptions1. The maximum attendance is7,500 people. The attendance decreases linearly with the increase in snowfall3. The data provided is accurate and sufficient for a linear regression model

STEP 2

We will use the method of least squares to find the best fit line for the given data. The formula for the slope (m) of the best fit 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 values- $\sum x$ is the sum of x values- $\sum y$ is the sum of y values- $\sum x^2$ is the sum of squares of x values

STEP 3

Let's calculate the necessary sums for the formula. We denote "Inches of Snow" as x and "Attendance" as y.$$\sum x =14 +0 +7 +2 +6 +1 +10$$$$\sum y =0 +7500 +401 +6539 +5126 +7500 +1200$$$$\sum xy =14<em>0 +0</em>7500 +7<em>401 +2</em>6539 +6<em>5126 +1</em>7500 +10*1200$$$$\sum x^2 =14^2 +0^2 +7^2 +2^2 +6^2 +1^2 +10^2$$

STEP 4

Now, plug in the values into the formula for the slope.
$$m = \frac{7(\sum xy) - (\sum x)(\sum y)}{7(\sum x^2) - (\sum x)^2}$$

STEP 5

The formula for the y-intercept (b) of the best fit line is$$b = \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{n(\sum x^2) - (\sum x)^2}$$

STEP 6

Now, plug in the values into the formula for the y-intercept.
$$b = \frac{(\sum y)(\sum x^2) - (\sum x)(\sum xy)}{(\sum x^2) - (\sum x)^2}$$

STEP 7

The equation of the best fit line is$$Attendance = m * (Inches\, of\, Snow) + b$$

STEP 8

To predict the attendance at a concert when there are.1 inches of snow on the ground, plug in the value of.1 for "Inches of Snow" in the equation.
$$Predicted\, Attendance = m *.1 + b$$

Round the predicted attendance to the nearest integer.