Answer:
a) To find a model for the cost, C, in dollars in terms of k, the number of kWh used, we can use linear regression to fit a line to the data points. The model can be represented as C = mk + b, where m is the slope and b is the y-intercept.
Using the given data points:
May: (1311, 202.915)
June: (1483, 228.75)
July: (1996, 305.70)
August: (2074, 317.40)
September: (2084, 318.90)
We can use linear regression to find the values of m and b that best fit the data.
b) We know the model fits the data if the linear regression line closely follows the data points and has a high coefficient of determination (R-squared value). Additionally, we can calculate the residuals (the differences between the actual data points and the predicted values from the model) to assess how well the model fits the data. If the residuals are small and randomly distributed, it indicates a good fit.
After obtaining the model for C in terms of k, we can compare the predicted costs with the actual costs for the given months to further validate the model's accuracy.
Step-by-step explanation:
