I need help solving this. I do not get it one bit.
The median home sale price in country A has been rising approximately linearly since 1995. The median home sale price in 1995 was $110,500. The median home sale price in 2004 was $194,200. Let P be the median home sale price and let t be the number of years since 1995.
Determine a function P(t) that fits this data.
how much did prices rise over how many years? ... this is the slope of the line
... price rise / years
t is the number of years
... it starts at a price in 1995 and increases some amount per year (slope)
To determine a function that fits the given data, we can use the concept of linear regression. Linear regression is a statistical method used to find the best-fitting line through a set of data points.
In this case, we have two data points: (1995, $110,500) and (2004, $194,200). Let's use these data points to find the equation of the line.
Step 1: Find the slope of the line
The slope of the line is given by the formula:
slope = (change in y) / (change in x)
change in y = $194,200 - $110,500 = $83,700
change in x = 2004 - 1995 = 9
slope = $83,700 / 9 ≈ $9300
Step 2: Find the y-intercept of the line
The y-intercept is the value where the line intersects the y-axis, which is the median home sale price when t = 0 (in the year 1995).
y-intercept = $110,500
Step 3: Write the equation in slope-intercept form
The equation of the line in slope-intercept form is:
y = mx + b
where:
y is the dependent variable (median home sale price)
x is the independent variable (number of years since 1995)
m is the slope
b is the y-intercept
Substituting the values we found:
P(t) = $9300t + $110,500
Therefore, the function P(t) that fits this data is:
P(t) = $9300t + $110,500