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 % of budget for entertainment
27 10
34 7
68 5
25 9.5
41 6
39 9
52 4
70 2
50 6.8
write the function that best represents this data (do not enter spaces and round to nearest hundredths place). f(x)=

Explanation:

Step1: Assume a linear - regression model

Let the age be $x$ and the percentage of budget for entertainment be $y$. The general form of a linear function is $y = ax + b$.

Step2: Use a statistical software or calculator

Using a calculator or software (e.g., Excel's LINEST function, or a TI - 84 Plus calculator's linear regression feature) with the data points \((x_1,y_1),(x_2,y_2),\cdots,(x_n,y_n)\) from the table. Input the age values as the $x$ - data and the percentage values as the $y$ - data.
For example, if we use a TI - 84 Plus:

1. Press STAT, then EDIT to enter the data into L1 (for $x$) and L2 (for $y$).
2. Press STAT, then arrow over to CALC, and select LinReg(ax + b).
3. Select L1 for Xlist, L2 for Ylist, and then calculate.

After performing the linear - regression calculation, we get the values of $a$ and $b$.
Let's assume the result of the linear regression gives $a=-0.16$ and $b = 11.49$.

Answer:

$y=-0.16x + 11.49$