uestion $6(20$ pts$)$ Using the data below, which represent the measured temperatures of a metal rod under varying heat inputs, perform the following tasks: a$)$ a$)$ Calculate the least$-$squares estimates of the thermal response constant and the initial temperature of the metal rod. b$)$ b$)$ Write the equation of the least$-$squares line. $($Note: Provide detailed hand calculations and compare with the Excel results.$)$ c$)$ c$)$ Compute the coefficient of determination $($R$^2).($Note: Provide a graph to be plotted only by Excel.$)$ Question $6(20$ pts$)$

Using the data below, which represent the measured temperatures of a metal rod under varying heat inputs, perform the following tasks:

a$)$ a$)$ Calculate the least$-$squares estimates of the thermal response constant and the initial temperature of the metal rod.

b$)$ b$)$ Write the equation of the least$-$squares line. $($Note: Provide detailed hand calculations and compare with the Excel results.I

c$)$ c$)$ Compute the coefficient of determination $(\backslash (\backslash$mathrm$\{$R$\}^\{2\}\backslash )).($Note: Provide a graph to be plotted only by Excel.$)$