Chapter 4, Problem 49SGR

To determine

To Find:

An equation of the regression line and estimate the daily sales on day 10 of the sale.

Answer to Problem 49SGR

The required equation of the regression line is :

  $y=5.36x+11$

Daily sales on day 10 of the sale = $65

Explanation of Solution

Given Information:

The table shows the number of sales made at an outerwear store during a sale.

  

Calculation:

Let

x -axis = days since sale began

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

CALCULATION SUMMARY

Sum of X = 28

Sum of Y = 227

Mean X = 4

Mean Y = 32.4286

Sum of squares ( SS_X ) = 28

Sum of products ( SP ) = 150

Regression Equation = y = bX + a

  

  

So, the regression equation is :

  $y=5.36x+11$

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

  $\begin{array}{l}y=5.36x+11\\ y=5.36(10)+\mathrm{11...................}[x=10]\\ y=53.6+11\\ y=64.6\approx 65\end{array}$

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