the table represents the results of survey that asked people their age and the percent of their budget that…

the table represents the results of survey that asked people their age and the percent of their budget that they spend on entertainment.\nage % of budget for entertainment\n27 10\n34 7\n68 5\n25 9.5\n41 6\n39 9\n52 4\n70 2\n50 6.8\nwrite the function that best represents this data (do not enter spaces and round to nearest hundredths place). f(x)=

the table represents the results of survey that asked people their age and the percent of their budget that they spend on entertainment.\nage % of budget for entertainment\n27 10\n34 7\n68 5\n25 9.5\n41 6\n39 9\n52 4\n70 2\n50 6.8\nwrite the function that best represents this data (do not enter spaces and round to nearest hundredths place). f(x)=

Answer

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:

$y=-0.16x + 11.49$