Question

4. Use technology to determine the equation of the line of best fit for the table of points below. Round any decimal values to two decimal places

Answer 1

Answer:

y = 1.61x - 17.70

Explanations:

To calculate the line of best fit from a table, follow the following steps:

Step 1:Caculate the means of x and y

`\begin{gathered} \bar{x}=\text{ }(\sum x)/(n) \\ \bar{x}=\text{ }(5+6+14+15+21+23+24)/(7) \\ \bar{x}\text{ = }(108)/(7) \\ \bar{x}\text{ = }15.43 \end{gathered}`
`\begin{gathered} \bar{y}\text{ = }(\sum y)/(n) \\ \bar{y}\text{ = }(-14-4+6+7+15+17+23)/(7) \\ \bar{y}\text{ = }(50)/(7) \\ \bar{y}\text{ = }7.14 \end{gathered}`

Step 2: Calculate the slope of the line of best fit

`m\text{ = }\frac{\sum (x_i-\bar{x})(y_i-\bar{y})}{\sum (x_i-\bar{x})^2}`

`\begin{gathered} m\text{ = }(581.57)/(361.71) \\ m\text{ = }1.61 \end{gathered}`

Step 3: Calculate the y-intercept, c, using the formula below:

`\begin{gathered} c\text{ = }\bar{y}-m\bar{x} \\ c\text{ = 7.14-1.61(15.43)} \\ c\text{ = }-17.70 \end{gathered}`

Step 4: Substitute the values of m and c into the slope - intercept form of the equation of a line:

y = mx + c

y = 1.61x - 17.70

The equation of the line of best fit is y = 1.61x - 17.70