Question

How do I solve this correctly?

Answer 1

The equation of the line of best fit and the slope and y-intercept of the equation are;

a. y = -0.0041·x + 16.03

b. The slope, -0.0041 indicates the amount of storage taken by additional music played on the device

The y-intercept represents the memory size of the music playing device, which is about 16.03 gigabyte

What is a line of best fit?; A line of best fit is a straight line that is drawn closest to the majority all the data points plotted the coordinate plane.

The first difference of the x- and y-values in the table are different, however a plot of the data on the coordinate plane shows a strong negative correlation between the x and y-values

The line of best fit can be found by using the least squares regression equation,
`\hat{y}` = a + b·x

Where;

`b = \frac{\sum(x - \bar{x})* (y-\bar{y})}{\sum(x - \bar{x})^2}`

`\bar{x}` = The average of the x-values

`\bar{y}}` = The average of the y-values

The table of values indicates;

`\bar{x}` ≈ 548.83

`\bar{y}` ≈ 13.783

`\sum(x - \bar{x})* (y-\bar{y})}` = -2884.12

`{\sum(x - \bar{x})^2}` = 706526.8

Therefore; b is; -2884.12/706526.8 ≈ -0.0041

The equation;
`\bar{y}}` = a + b·
`\bar{x}`, indicates that we get;

13.783 = a + -0.0041 × 548.83

a = 13.783 + 0.0041 × 548.83

13.783 + 0.0041 × 548.83 ≈ 16.03

a ≈ 16.03

The equation is therefore;

`\hat{y}` = -0.0041·x + 16.03

b. The slope, b ≈ -0.0041 indicates that the storage reduces by 0.0041 gigabytes for each song added on the device

The y-intercept indicates that the initial storage available on the music playing device is about 16.03 gigabytes