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

the table represents the results of survey that asked people their age and the percent of their budget that they spend on entertainment.\n|age|27|34|68|25|41|39|52|70|50|\n|% of budget for entertainment|10|7|5|9.5|6|9|4|2|6.8|\nwrite the function that best represents this data (do not enter spaces and round to nearest hundredths place).\nf(x)=

Answer

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)