Question

john sells frozen fruit bars at a stand in a park during the summer months. he records the average weekly temperature and number of frozen fruit bars sold for 6 weeks.
what type of correlation exists between the temperature and the number of fruit bars sold?
what is the real - world meaning of the slope of the line of best fit for the given scenario?
there are approximately more fruit bars sold for every degree temperature rises.

Explanation:

Step1: Calculate the slope using two - point formula

The formula for the slope \(m=\frac{y_2 - y_1}{x_2 - x_1}\). Let's take two points \((x_1,y_1)=(67,50)\) and \((x_2,y_2)=(87,100)\).

$$m=\frac{100 - 50}{87 - 67}=\frac{50}{20}=2.5$$

Another way: Using the general linear regression formula \(y = mx + b\). But for a rough estimate, using two - point formula. If we take \((71,54)\) and \((87,100)\)

$$m=\frac{100 - 54}{87 - 71}=\frac{46}{16}=2.875$$

If we use all the data points in a regression calculator (assuming basic linear regression concept where slope represents the change in \(y\) (number of fruit bars) per unit change in \(x\) (temperature)).
The slope of the line of best fit in a linear regression model \(y=mx + b\) (where \(y\) is the number of fruit bars sold and \(x\) is the temperature) represents the change in the number of fruit bars sold per degree change in temperature.

Answer:

2.2