Chapter 6.4, Problem 2E

To determine

To find: The best fit curve of the data.

Answer to Problem 2E

  $m_{cubic}=-0.0003x^3-0.0913x^2+8.7817x-135.59$

Explanation of Solution

Given: The table shows number minutes out of 8 hours work day.

  $\begin{array}{cccccccccc}\text{Year}& 1930& 1940& 1950& 1960& 1970& 1980& 1990& 2000& 2005\\ t& 30& 40& 50& 60& 70& 80& 90& 100& 105\\ \text{Minutes,}m& 56& 86& 119& 134& 144& 147& 148& 163& 151\end{array}$

In table shows number of minutes out of each eight- hour work day for various years.

Let t =30 represents year corresponding to 1930 .

Now plot the scatter plot and draw each regression on graph.

  

Using graph the equation of regression,

Linear regression, $m_{linear}=1.1922t+44.764$ and coefficient of regression, $r^2=0.8126$

Quadratic regression, $m_{qua}=-0.0255x^2+4.6838x-58.674$ and coefficient of regression, $r^2=0.9747$

Cubic regression, $m_{cubic}=-0.0003x^3-0.0913x^2+8.7817x-135.59$ and coefficient of regression, $r^2=0.9846$

So, coefficient of regression constant is nearest to 1 for cubic regression. Best fit curve would be cubic.

Hence, the best fit curve for the given data is cubic,

  $m_{cubic}=-0.0003x^3-0.0913x^2+8.7817x-135.59$