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The table shows the relationship between the daily temperature (1) and the daily attendance (A) at a local pool. Pool Attendance and Temperature Temperature (°F)82 80 84 95 90 88 80 80 86Attendance 510 500 510 580 550 540 500 510 520 Which function best represents the relationship in the data obtained using linear regression?O A = St + 100 O A= 4 + 200 O A = 5.5t + 60 O A = 2.5t + 300

User Pubudu Jayawardana
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1 Answer

18 votes
18 votes

Final answer:

To find the best-fit linear function representing pool attendance based on temperature using linear regression, the student should enter the data into a calculator, create a scatter plot, use the regression function to find the least-squares regression line and evaluate the fit using the coefficient of determination and residuals.

Step-by-step explanation:

The student is asking how to generate a best-fit linear function based on the given data using linear regression. To accomplish this, the student would perform the following steps:

  1. Enter the data into a calculator or statistical software to create a scatter plot.
  2. Apply the calculator's regression function to calculate the equation of the least-squares regression line. Add this line to your scatter plot from Part A.
  3. The slope of the regression line indicates the estimated increase in attendance for each 1°F increase in temperature. The y-intercept represents the estimated pool attendance when the temperature is 0°F, which in this context, might not have a practical interpretation.
  4. To determine how well the regression line fits the data, you would look at the coefficient of determination (r²), which indicates the proportion of variance in the dependent variable (attendance) that is predictable from the independent variable (temperature).
  5. The point with the largest residual is the one where the actual attendance deviates most from the predicted attendance by the regression line. The residual is the difference between the observed value and the value predicted by the regression line. Whether this point is an outlier or influential depends on its effect on the regression analysis.

User Iqbalzas
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