Given
The data,
To find:
1) The equation of the line of best fit.
2) The time when the player can do 22 leg press repetitions.
Explanation:
It is given that,
That implies,
The equation of the line of best fit is given by,
[tex]T=kL+b[/tex]
Then,
[tex]k=\frac{\bar{LT}-\bar{L}\bar{T}}{\bar{L^2}-(\bar{L})^2},\text{ }b=\bar{T}-k\bar{L}[/tex]
Therefore,
[tex]\begin{gathered} \bar{L}=\frac{12+32+11+7+23+28+15}{7} \\ =\frac{128}{7} \\ =18.3 \end{gathered}[/tex]
Also,
[tex]\begin{gathered} \bar{T}=\frac{8.6+14.6+7.1+8.3+11.9+13.4+9.5}{7} \\ =\frac{73.4}{7} \\ =10.5 \end{gathered}[/tex]
Also,
[tex]\begin{gathered} \bar{L^2}=\frac{12^2+32^2+7^2+11^2+23^2+28^2+15^2}{7} \\ =\frac{2876}{7} \\ =410.9 \end{gathered}[/tex]
Also,
[tex]\begin{gathered} \bar{LT}=\frac{12\times8.6+32\times14.6+7\times7.1+11\times8.3+23\times11.9+28\times13.4+15\times9.5}{7} \\ =\frac{1502.8}{7} \\ =214.7 \end{gathered}[/tex]
That implies,
[tex]\begin{gathered} k=\frac{214.7-(18.3\times10.5)}{410.9-(18.3)^2} \\ =\frac{214.7-192.15}{410.9-334.89} \\ =\frac{22.55}{76.01} \\ =0.3 \end{gathered}[/tex]
And,
[tex]\begin{gathered} b=\bar{T}-k\bar{L} \\ =10.5-(0.3\times18.3) \\ =10.5-5.49 \\ =5 \end{gathered}[/tex]
Hence, the equation of the best line of fit is,
[tex]T=0.3L+5[/tex]
And, the time taken when L=22 is,
[tex]\begin{gathered} T=0.3(22)+5 \\ =6.6+5 \\ =11.6 \end{gathered}[/tex]
Hence, the time taken to complete 22 Leg press repetition is 11.6.
