Answer:
P(t) = 15t + 230
Explanation:
We are given two points on the line: (2, 260) and (3, 275)
To find the slope, use the formula:
Slope = (y2 - y1) / (x2 - x1)
Where:
y2 = 275 (price at year 3)
y1 = 260 (price at year 2)
x2 = 3 (year 3)
x1 = 2 (year 2)
Plug into the slope formula:
Slope = (275 - 260) / (3 - 2) = 15 / 1 = 15
The equation of a line is:
y = mx + b
Where m is the slope (15) and b is the y-intercept.
To find b, substitute the slope and a point into the equation:
260 = 15(2) + b
260 = 30 + b
b = 260 - 30 = 230
Therefore, the equation of the best fit line is:
P(t) = 15t + 230
Where P is price in thousands and t is years since 2018.
Is there a way to measure how accurate this best fit line is in predicting future prices?
Yes, there are a few ways to measure how accurate the best fit line model will be in predicting future home prices. Firstly, calculate the R-squared (R2) value. R2 indicates how well the regression line approximates the real data points. The closer R2 is to 1, the better the line fits the data. Secondly, compare future real data points to predictions from the line. Calculate the error (difference between predicted and actual values) to see how far off the line's estimates are. Thirdly, perform a residual analysis on the existing data. The residuals are the differences between actual and fitted values. Lower/random residuals indicate a better linear fit. Fourthly, develop a forecast interval based on standard error of the regression. This gives a range the future values are likely to fall within, accounting for uncertainty. For time series data, also consider other forecasting techniques like moving averages to compare predictive power. Collect additional future data points over time and re-evaluate the line's fit. As more real data emerges, the accuracy of the model can be continually assessed.
Regularly checking these accuracy metrics as new price points occur would allow Marcus to determine how well or poorly this simple linear model performs at predicting future home value trends.
Thanks.