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	6	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 formula

We can use a statistical software or a calculator with linear - regression capabilities. Let \(x\) be the age and \(y\) be the percentage of budget for entertainment. The general form of a linear regression equation is \(y = ax + b\), where \(a\) is the slope and \(b\) is the y - intercept.

Step2: Calculate slope \(a\) and y - intercept \(b\)

Using a calculator or software (e.g., in Excel with the LINEST function, or on a TI - 84 Plus: Stat > Edit to enter data, then Stat > Calc > LinReg(ax + b)), for the given data points \((x_1,y_1),(x_2,y_2),\cdots,(x_n,y_n)\) where \(n = 9\). After performing the linear regression calculation, we get \(a\approx - 0.13\) and \(b\approx13.47\).

Answer:

\(f(x)=-0.13x + 13.47\)