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Using the data in this table, what would be the line ofbest fit ( rounded to the nearest tenth)?

Using the data in this table, what would be the line ofbest fit ( rounded to the nearest-example-1
User Nick Chubb
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1 Answer

3 votes

Solution

Note: The formula to use is


y=mx+b

Where m and b are given by

the b can also be given as


b=\bar{y}-m\bar{x}

The table below will be of help

We have the following from the table


\begin{gathered} \sum_^x=666 \\ \sum_^y=106.5 \\ \operatorname{\sum}_^x^2=39078 \\ \operatorname{\sum}_^xy=6592.5 \\ n=10 \end{gathered}

Substituting directing into the formula for m to obtain m


\begin{gathered} m=(10(6592.5)-(666)(106.5))/(10(39078)-(666)^2) \\ m=(-5004)/(-52776) \\ m=0.09481582538 \\ m=0.095 \end{gathered}

to obtain b


\begin{gathered} \bar{y}=\frac{\operatorname{\sum}_^y}{n} \\ \bar{y}=(106.5)/(10) \\ \bar{y}=10.65 \\ and \\ \bar{x}=\frac{\operatorname{\sum}_^x}{n} \\ \bar{x}=(666)/(10) \\ \bar{x}=66.6 \end{gathered}

Therefore,


\begin{gathered} b=\bar{y}- m\bar{x} \\ b=10.65-(0.095)(66.6) \\ b=4.323 \end{gathered}

Therefore,


\begin{gathered} y=mx+b \\ y=0.095x+4.323 \end{gathered}

To the nearest tenth


y=0.1x+4.3

The least square method didn't give an accurate answer, so we use a graphing tool to estimate instead

Here

m = 0.5 (to the nearest tenth)

b = -23.5 (to the nearest tenth)

The answer is


\begin{gathered} y=mx+b \\ y=0.5x-23.5 \end{gathered}

Using the data in this table, what would be the line ofbest fit ( rounded to the nearest-example-1
Using the data in this table, what would be the line ofbest fit ( rounded to the nearest-example-2
Using the data in this table, what would be the line ofbest fit ( rounded to the nearest-example-3
Using the data in this table, what would be the line ofbest fit ( rounded to the nearest-example-4
User Gabbler
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4.3k points