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Q49.

Expert-verified

Algebra 1

Found in: Page 273

Book edition Student Edition

Author(s) Carter, Cuevas, Day, Holiday, Luchin

Pages 801 pages

ISBN 9780078884801

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Short Answer

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 sale
Days Since Sale Began
1
2
3
4
5
6
7
Daily Sales ( $$$ )
15
21
32
30
40
38
51

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

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

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.

$\begin{array}{l} Sum of X = 28 \\ Sum of Y = 227 \\ Mean X = 4 \\ Mean Y = 32 .4286 \\ Sum of squares (S S_{X}) = 28 \\ Sum of products (S P) = 150 \end{array}$

Regression Equation: $ŷ = b X + a$

role="math" localid="1647412399173" $\begin{array}{l} b = S P / S S_{X} = 150 / 28 = 5.35714 \\ a = M_{Y} - b M_{X} = 32.43 - (5.36 \times 4) = 11 \\ y = 5.35714 X + 11 \end{array}$

Step 3. Plot the graph.

Graph the line $\hat{y} = 5.35714 X + 11$ with slope $a$ and intercept $b$ .

Thus, the regression equation is $\hat{y} = 5.36 X + 11$ .

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 :

$\begin{matrix} \hat{y} = 5.36 X + 11 \\ \hat{y} = 5.36 (10) + 11 \\ \hat{y} = 53.6 + 11 \\ \hat{y} = 64.6 \approx 65 \end{matrix}$

So, the daily sales on day 10 of the sale = $$$ 65.

Most popular questions for Math Textbooks

The table below shows the relationship between certain temperatures in degrees Fahrenheit and degrees Celsius. Which of the following linear equations correctly models the relationship?

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$10 °$	$50 °$
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