Math

QuestionA concert venue seats 7,500. Analyze snow vs. attendance data, then: (a) Is a linear model suitable? Yes/No (b) Find slope and yy-intercept: Attendance == (Inches of Snow) + (c) Predict attendance with 9.1 inches of snow: ×\times people.

Studdy Solution

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 ism=n(xy)(x)(y)n(x2)(x)2m = \frac{n(\sum xy) - (\sum x)(\sum y)}{n(\sum x^2) - (\sum x)^2}where- n is the number of data points- xy\sum xy is the sum of the product of x and y- x\sum x is the sum of x- y\sum y is the sum of y- x2\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 x\sum x, y\sum y, xy\sum xy, and x2\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 isb=ym(x)nb = \frac{\sum y - m(\sum x)}{n}where- m is the slope- n is the number of data points- x\sum x is the sum of x- y\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 formAttendance=m(Inches of Snow)+bAttendance = m(\text{Inches of Snow}) + bwhere 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.

STEP 9

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

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