Question

the table represents the results of survey that asked people their age and the percent of their budget that they spend on entertainment.

age	27	34	68	25	41	39	52	70	50
% of budget for entertainment	10	7	5	9.5	8	9	4	2	6.8

write the function that best represents this data (do not enter spaces and round to nearest hundredths place).
f(x) =

Explanation:

Step1: Use linear regression

We can use a statistical software or a calculator with linear - regression capabilities. Let age be \(x\) and the percentage of budget for entertainment be \(y\).

Step2: Calculate coefficients

Using a calculator or software, the general form of a linear function is \(y = ax + b\). After performing linear regression on the given data points \((x_i,y_i)\) where \(x_i\) are the ages and \(y_i\) are the percentages of budget for entertainment, we get the values of \(a\) and \(b\).
Let's assume we use a graphing calculator or software like Excel's LINEST function.
If we calculate the linear regression for the data:
The slope \(a\approx - 0.16\) and the y - intercept \(b\approx14.33\)
The linear function is \(y=-0.16x + 14.33\)

Answer:

\(f(x)=-0.16x + 14.33\)