The following are measured values of a system temperature versus time: 

(a) Use the method of least squares Appendix A.1 to fit a straight line to the data, showing your calculations. You may use a spreadsheet to evaluate the formulas in Appendix A.1, but do not use any plotting or statistical functions. Write the derived formula for T(t), and convert it to a formula for t(T). 

(b) Transfer the data into two columns on an Excel spreadsheet, putting the t data (including the heading) in Cells A1–A7 and the T data (including the heading) in B1–B7. Following instructions for your version of Excel, insert a plot of T versus t into the spreadsheet, showing only the data points and not putting lines or curves between them. Then add a linear trendline to the plot (that is, fit a straight line to the data using the method of least squares) and instruct Excel to show the equation of the line and the R 2 value. The closer R 2 is to 1, the better the fit. 

Appendix A.1

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t(min) 0.0 2.0 4.0 6.0 8.0 10.0 T('°C) 25.3 26.9 32.5 35.1 36.4 41.2