Question

a toy company is studying the average demand for one of their new dolls based on its price. the results are presented in the table below. use technology to find the line of best fit for the data. then use that model to predict the number of people who will buy the doll will have if its price is $10. round to the nearest person.

Explanation:

Step1: Input data into technology

Input the price values (1, 2, 4, 6, 7, 8) as the \(x\)-values and the buyer values (60.36, 50.14, 34.54, 39.6, 41, 29.91) as the \(y\)-values into a graphing calculator or statistical software.

Step2: Find the line of best fit

Using linear regression on the data, the line of best fit is \(y=-3.3x + 63.1\) (the technology calculates the slope \(m\approx - 3.3\) and the \(y\)-intercept \(b\approx63.1\) based on the least - squares method \(y = mx + b\)).

Step3: Predict for \(x = 10\)

Substitute \(x = 10\) into the equation \(y=-3.3x + 63.1\).

$$y=-3.3\times10+63.1=-33 + 63.1=30.1$$

Answer:

30