Quandaries
and Queries 

Who is asking: Other Question: I WOULD appreciate it Hooke's Law asserts that the magnitude
of the force required to hold a spring is a linear function of the
extension e of the spring. That
is, e: 9 , 11 , 12 , 16 , 19 FIND the least square line f= B_{0} + B_{1}x approximating this data and use it to approximate k. 

Hi, There are a number of equivalent expressions for finding B_{0} and B_{1} in the least squares line y = B_{0} + B_{1}x. In your case the independent variable is e rather than x, the dependent variable is f rather than y and the constants are e_{0} and k rather than B_{0} and B_{1}.The formulas I use are and Let's look at your data, changing the variable names from e and f to x and y. You are asked to find k which is the coefficient of e in the equation. After our change of variables to x and y the coefficient of x is B_{1}. You have n = 5. To use the expressions above I need the sum of all the x's, the sum of the y's, the sum of the x^{2}'s and the sum of the x's times the y's. I am going to put your data in a table and calculate these sums.
The numbers in the bottom row of the table are the sums of the columns. Hence
Now use the expression for B_{1} above to find the value of k. Penny


