 Suggested languages for you:

Europe

Answers without the blur. Sign up and see all textbooks for free! Q49.

Expert-verified Found in: Page 273 ### Algebra 1

Book edition Student Edition
Author(s) Carter, Cuevas, Day, Holiday, Luchin
Pages 801 pages
ISBN 9780078884801 # The table shows the number of sales made at an outerwear store during a sale. Write an equation of the regression line. Then estimate the daily sales on day 10 of the saleDays Since Sale Began1234567Daily Sales ()15213230403851

The required equation of the regression line is: $\mathbit{y}\mathbf{=}\mathbf{5}\mathbf{.36}\mathbit{x}\mathbf{+}\mathbf{11}$. The daily sales on day 10 of the sale is 65.

See the step by step solution

## Step 1. Rearrange the table.

Let

$X$-axis = days since sale begin.

$Y$-axis = daily sales ().

Using the regression calculator to find the equation of the regression line:

 Days since sale began ($x$) Daily Sales ($y$) 1 15 2 21 3 32 4 30 5 40 6 38 7 51

## Step 2. Find the regression equation.

$\begin{array}{l}\text{Sum of}X=28\\ \text{Sum of}Y=227\\ \text{Mean}X=4\\ \text{Mean}Y=32.4286\\ \text{Sum of squares}\left(S{S}_{X}\right)=28\\ \text{Sum of products}\left(SP\right)=150\end{array}$

Regression Equation: $ŷ=bX+a$

role="math" localid="1647412399173" $\begin{array}{l}b=SP/S{S}_{X}=150/28=5.35714\\ a={M}_{Y}-b{M}_{X}=32.43-\left(5.36×4\right)=11\\ y=5.35714X+11\end{array}$

## Step 3. Plot the graph.

Graph the line $\stackrel{^}{y}=5.35714X+11$ with slope $a$ and intercept $b$. Thus, the regression equation is $\stackrel{^}{y}=5.36X+11$.

## Step 4. Put the value of X to find the estimated sales.

Substituting the value of $x=10$ in regression equation to find the daily sales on day 10 of the sale :

$\begin{array}{c}\stackrel{^}{y}=5.36X+11\\ \stackrel{^}{y}=5.36\left(10\right)+11\\ \stackrel{^}{y}=53.6+11\\ \stackrel{^}{y}=64.6\approx 65\end{array}$

So, the daily sales on day 10 of the sale = 65. ### Want to see more solutions like these? 