Question

1. the red star clothing emporium sells a lot of levi strauss blue jeans. store management wants to examine the impact price has on the sales volume of jeans.here is the sales data for seven days at various prices of blue jeans. price (in dollars) per pair demand (number of pairs sold) 20 60 22 57 23 53 23 56 27 52 29 49 30 44 rounded to the nearest hundredth, what is the equation of the line of best fit?

Explanation:

Step1: Calculate the means of \(x\) (price) and \(y\) (demand)

Let \(x\) be the price and \(y\) be the demand.
\(\bar{x}=\frac{20 + 22+23+23+27+29+30}{7}=\frac{174}{7}\approx24.86\)
\(\bar{y}=\frac{60 + 57+53+56+52+49+44}{7}=\frac{371}{7}\approx53\)

Step2: Calculate the slope \(m\)

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\(m=\frac{-116.0}{86.86}\approx - 1.34\)

Step3: Calculate the \(y\)-intercept \(b\)

Using the formula \(y=mx + b\), substitute \(m\approx - 1.34\), \(x = \bar{x}\approx24.86\), and \(y=\bar{y}\approx53\)
\(53=-1.34\times24.86 + b\)
\(b=53+1.34\times24.86\)
\(b=53 + 33.31\)
\(b\approx86.31\)

Answer:

\(y=-1.34x + 86.31\)