Question

A coffee shop takes daily data on the high temperature for the day in degrees F, and the number of cups of hot chocolate sold. They construct a scatterplot and examine the linear relationship.The least squares regression line equation is:
y=76.42-1.38x

(1)Using the slope value, describe the relationship in context.

(2)Can this line equation be used to make a prediction for number of cups of hot chocolate sold when it's 60 degrees F outside? Explain.

Answer 1

Let the temperature for the day in degree F be denoted by x

And let the number of cups of hot chocolate sold be denoted by y

Here x is independent variable and y is the dependent variable in the equation so, we denote the temperature for day with x as temperature of day is independent of the number of cups of hot chocolate sold.

Now from the scatter plot we know that there is a linear relation between x and y

1. Regression Line :

y= 76.42 - 1.38x

Here slope is -1.38

We can find the slope of a linear regression line by 1^st arranging the equation in

y=mx + c form where m is the slope and c is the intercept.

So if we arrange our equation in this form we get

y= (-1.38)x + 76.42

Therefore, we get slope as -1.38

Answer: Now as the slope value is -1.38 , which is a negative value and as we already know there is linear relation between x and y so we can say there is a negative linear relation between temperature for the day in degree F (x) and number of cups of hot chocolate sold (y) .That means as the temperature of the day increases the number of cups of hot chocolate sold will decrease linearly.

2. No this line equation can’t be used to make a prediction for number of cups of hot chocolate sold when its 60 degree F outside (means x= 60)

Because if we put the value of x=60 in the regression equation we get:

    y= 76.42 – (1.38 * 60)

    or y= -6.38

y means number of cups of hot chocolate sold which can’t be negative quantity, at least it has to be zero but when the temperature is 60 degree F number of cups sold is -6.38 which is impossible(as negative)

therefore, this line equation can’t be used to make prediction for number of cups of hot chocolate sold when the temperature is 60 degree F outside.