Develop a calibration curve for the bathroom scale using the data provided in Table $1$ below. Find the coefficients for your calibration curve using $1)$ the Trendline feature in Microsoft Excel, $2)$ Linear Regression, and $3)$ Least Squares Regression using optimization. Use the videos and lab manual associated with regression to assist you.

Do the three methods provide the same results? Why or why not? What would be the true weight for a scale reading of $170lbs?$

$1$

Table $1-$ Data for Bathroom Scale Calibration Curve

$\backslash$table$[[\backslash$table$[[$True Weight$],[($Lbs$)]],\backslash$table$[[$Scale Reading$],[($Lb$)]]],[150,147\mathrm{.}5],[155,152\mathrm{.}5],[160,157\mathrm{.}5],[165,162\mathrm{.}4],[170,167\mathrm{.}4],[175,172\mathrm{.}4],[180,177\mathrm{.}3],[185,182\mathrm{.}3],[190,187\mathrm{.}2],[195,192\mathrm{.}2],[200,197\mathrm{.}2]]$