The manager of a small nature park found the regression line for the weekly prof

Question

The manager of a small nature park found the regression line for the weekly profits, p in dollars, as a function of the number of visitors, n, was p = 6n-2700. (a) How much profit is predicted if 500 people visit the park in a week? A profit of $ (b) Explain the meaning of the slope of the regression line in the context of this problem. Include units. The slope o is predicted. means that for every weekly visitor, the profit by S The units are (c) Explain the meaning of the vertical intercept of the regression line in the context of this problem. Include units. means that when the number of weekly visitors is zero, the park has a The vertical intercept of of S The units are (d) How many weekly visitors does the park need if it is not to lose money? The park needs weekly visitors

Explanation / Answer

The regression line is given as

P= 6n-2700

Where p is profit in dollars, n is count of visitors in a week.

A) if visitor count = 500, then what is the profit.

We can substitute the value of n = 500 and get the value of p

This means p = 6*500-2700

p= 3000-2700

p= 300

So the profit in this case is 300 dollars.

B) Slope of the regression line indicates change in the value of the dependent variable (in this case it's profit, p), due to an increment of 1 unit in the independent variable (in this case number of weekly visitors, n). Slope of the regression line is positive 6, which means that profit grows if weekly visitor count grows in a ratio of 6:1

Thus, the slope of 6 means that for every weekly visitor, the profit increases by 6 dollars.

C) A vertical intercept of a regression line, say y=m*x+c; means the value of y when the independent variable x is set to 0

In the given case, if we set n =0, the p= -2700. This means,

The vertical intercept of -2700 means that when the number of weekly visitors is zero, the park has a loss of 2700 dollars per week.

Units are dollars per week.

D) in order to ensure that the park does not lose money, we should find out what is the number of visitors required to make the profit,p= 0. This will be the minimum count needed.

Solving by setting p=0, we get

6n-2700=0

6n-2700+2700=0+2700

=> 6n = 2700

=> 6n/6 = 2700/6

=> n = 450

Thus the park needs at least 450 weekly visitors to ensure it doesn't lose money.

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