Question

Tara keeps track of the numbers of trips she takes to the library into the bookstore each month for a year. Her data are shown in the scatterplot below. Which equation represents a line of best fit for the date in the scatterplot? Is the correct answer ABC or D?

Answer 1

12 points are given on the plane

`\lbrace(1,6),(2,6),(2,5),(2,3),(3,5),(3,2),(4,4),(4,3),(4,1),(5,1),(6,1),(7,1)\rbrace`

Finding the mean of X and Y,

`\begin{gathered} M_x=(1+2+2+2+3+3+4+4+4+5+6+7)/(12)=3.5833 \\ and \\ M_y=(6+6+5+3+5+2+4+3+1+1+1+1)/(12)=3.4167 \end{gathered}`

Then, the sum of squares and the sum of products,

`\begin{gathered} SS_x=\sum_{n\mathop{=}0}^(12)(x_n-M_x)^2=34.9167 \\ and \\ S_(xy)=\sum_{n\mathop{=}0}^(12)(x_n-M_x)(y_n-M_y)=-23.9167 \end{gathered}`

x_n and y_n are the x and y

In general, the linear regression equation is given by the formula below

`\begin{gathered} y=bX+a \\ b=(S_(xy))/(SS_x) \\ and \\ a=M_y-bM_x \end{gathered}`

Therefore, in our case, calculating a and b,

`\begin{gathered} b=-(23.9167)/(34.9167)=-0.68496 \\ and \\ a=3.4167-(-0.68496)*3.5833=5.87112 \end{gathered}`

Thus, the line of best fit is

`\Rightarrow y=-0.68496x+5.89112`

Hence, the option that more resemble the equation above is the last option. The answer is y=-2x/3+6 2/3