The table shows the sales of a health and beauty supply company, in millions of dollars, for several years. Let x be the number

Question

1 year ago

15

The table shows the sales of a health and beauty supply company, in millions of dollars, for several years. Let x be the number

of years since 2010.
Year 2011 2012 2013 2014 2015
Sales 12.2 19.1 29.4 37.3 45.7

a. Write the equation for the best-fit line for the data. Round to the nearest hundredth, if necessary.

y =
x +

Part B
Select the correct choices to complete the sentence.
b. Find and interpret the correlation coefficient.

r ≈ , 1 of 4.
Select Choice

The equation , 2 of 4.
Select Choice
the data very well. Its , 3 of 4.
Select Choice
value means that as the years since 2010 increase, sales, in millions of dollars, , 4 of 4.
Select Choice
.

Mathematics

1 answer:

WITCHER [35] · Answer 1 · 2024-02-27T02:22:08+03:00

a. The equation for the line of best-fit is:

y = 8.52x + 11.7.

b. The correlation coefficient is of: 0.9987, hence there is a strong positive correlation between the variables.

<h3>How to find the equation of the line of best fit and the correlation coefficient?</h3>

To obtain the regression equation, also called line of best fit or least squares regression equation, we need to insert the points (x,y) in the calculator. These points are given on a table or in a scatter plot in the problem.

The points in this problem are given on the table as follows:

(0, 12.2), (1, 19.1), (2, 29.4), (3, 37.3), (4, 45.7).

As we consider the input x as the number of years since 2011.

Then, using the calculator, the equation is given as follows:

y = 8.52x + 11.7.

Using a correlation coefficient calculator, the numeric value of the coefficient is of:

r = 0.9987.

Hence the correlation between the variables is classified as follows: