Question

Alejandro is selling HDMI cables on eBay, and is trying to determine the best price to sell at. For the last 10 weeks, he has adjusted his price slightly each week and tracked the number of cables he sold. He plotted the results, and drew a line he feels fits the data well.

33.253.53.7544.254.54.75550100150200250Price ($)Quantity Sold

a) The line of best fit passes through the points (3.50, 210) and (4.75, 180). Find an equation for the line.

Use variables: p for price in dollars, and Q for quantity of cables sold.

   

b) Using this model, predict the number of cables Alejandro would sell at a price of $3.65, to the nearest whole cable.

cables

Answer 1

Answer:

a.

Let y = a + bx be the regression equation

where a is intercept and b is slope.

SLope = (y2 -y1) / (x2 - x1)

= 170 -210)/(4.75 -3.5)

=-32

then regression eqn can be written ads

y = a - 32x

by substituting the two pints in Y = a - 32 *x

a = 322

therefore y 322 - 32 *x

b.

for x = 3.65

y = 322 - 32 * 3.65 = 205.2(~ 205)