Question

Temperature (°C) Number of People Day х у 1 20 280 2 24 360 3 36 450 4 32 420 5 2 28 400 ON 38 500 7 34 475 8 26 520 Question: The table shows data for the number of people using a swimming pool over 8 days in summer, and the corresponding maximum temperature (in degrees Celsius) on each day. A Find the equation of the line of best fit for the data. Round decimals to the nearest tenth. B. Can a set of data have more than one line of best fit? Why or why not?

Answer 1

First Step: Calculate the mean of the values in X and Y

`\begin{gathered} \bar{x}=(20+24+36+32+28+38+34+26)/(8)=29.75 \\ \bar{y}=400.625 \end{gathered}`

Second step: we have to find the sum of Squares and sum of products

Third step: find the linear equation

`\begin{gathered} Y=aX+b, \\ a=(SP)/(SS)=(3201.25)/(275.5)=11.61978 \\ b=\bar{y}-a\cdot\bar{x}=54.93648 \\ Y=11.61978X+54.93648 \end{gathered}`