Question

The following are advertised sale prices of color televisions at Anderson's: Size (inches) Sales Price ($) 9 147 20 197 27 297 31 44735 1177 40 2177 60 2497The researcher wants to determine if their appears to be a relationship between the variables. Decide which variable should be the independent variable and which should be the dependent variable.

Answer 1

See below

Explanation:

The independent variable should be the size and the dependent variable the price.

This is the most logical approach if the manager wants to have an idea about what price could be adequate for future models with different sizes.

The first thing to do if we want to determine if there appears to be a relationship between the variables is to draw the scatter plot

(See picture attached)

From the scatter plot we can tell that there is an apparent directly proportional relationship between size and price (the larger the size, the larger the price).

We could now try and compute the Pearson correlation coefficient r given by

`\bf r=\displaystyle(n\displaystyle\sum x_iy_i-\displaystyle\sum x_i\displaystyle\sum y_i)/(√(n\displaystyle\sum x_i^2-(\displaystyle\sum x_i)^2)√(n\displaystyle\sum y_i^2-(\displaystyle\sum y_i)^2))`

where

`\bf x_i` are the sizes

`\bf y_i` are the prices

n = number of observations (7)

If we did so, we would find that r = 0.9, which tells us that there is a good linear correlation between size and price.