Year: 1990,1992, 1994, 1996, 1998, 2000, 2002, 2004, 2006
Attendance (millions): 254, 269, 265, 290, 300, 316, 323, 329, 336
Write an equation of the trend line, rounding to two decimal places as needed. For this problem, choose the points (1990, 254) and (2002, 323).
The slope of the trendline can be calculated using the formula:
slope = (y2 - y1) / (x2 - x1)
Using the points (1990, 254) and (2002, 323):
slope = (323 - 254) / (2002 - 1990)
slope = 69 / 12
The y-intercept can be calculated using the formula:
y-intercept = y - (slope * x)
Using the point (1990, 254):
y-intercept = 254 - (slope * 1990)
Now we can substitute the values into the slope equation:
slope = 69 / 12
y-intercept = 254 - (slope * 1990)
Therefore, the equation of the trendline is:
y = (69 / 12)x + (254 - (69 / 12) * 1990)
try again
I apologize for the mistake. Let's try again.
Using the points (1990, 254) and (2002, 323):
First, let's find the slope:
slope = (y2 - y1) / (x2 - x1)
slope = (323 - 254) / (2002 - 1990)
slope = 69 / 12
slope ≈ 5.75
Now, let's find the y-intercept using the point (1990, 254):
y = mx + b
254 = (5.75)(1990) + b
254 = 11442.5 + b
b = 254 - 11442.5
b ≈ -11188.5
Therefore, the equation of the trendline is:
y = 5.75x - 11188.5
Estimate the attendance at theme parks in the country in 2005.
The estimated attendance was ___ million
(Round to the nearest whole number as needed. Use the answer from the previous part to find this answer.)
To estimate the attendance at theme parks in the year 2005, we can use the trendline equation:
y = 5.75x - 11188.5
Plugging in x = 2005:
y = 5.75(2005) - 11188.5
y ≈ 11523.75
Rounding to the nearest whole number:
The estimated attendance at theme parks in the country in 2005 was approximately 11,524 million.
no
Apologies for the error. Let's recalculate.
Using the trendline equation:
y = 5.75x - 11188.5
Plugging in x = 2005:
y = 5.75(2005) - 11188.5
y ≈ 3638.75
To the nearest whole number:
The estimated attendance at theme parks in the country in 2005 was approximately 3639 million.
Square Feet:1511, 2512, 3007, 3015
Selling Price: $93,246, $229,000, $250,000, $265,000
A linear regression equation is ___
(Type an equation. Use integers or decimals for any numbers in the equation. Round to three decimal places as needed.)
To find the linear regression equation, we need to calculate the slope and y-intercept.
Using the given data points:
Square Feet: 1511, 2512, 3007, 3015
Selling Price: $93,246, $229,000, $250,000, $265,000
Let's calculate the slope using the formula:
slope = (n * ∑(x * y) - ∑x * ∑y) / (n * ∑(x^2) - ∑x^2)
where n is the number of data points.
First, calculate the necessary variables:
n = 4 (since there are 4 data points)
∑(x * y) = (1511 * 93246) + (2512 * 229000) + (3007 * 250000) + (3015 * 265000)
∑x = 1511 + 2512 + 3007 + 3015
∑y = 93246 + 229000 + 250000 + 265000
∑(x^2) = (1511)^2 + (2512)^2 + (3007)^2 + (3015)^2
Calculate the values:
∑(x * y) = 1416865588
∑x = 10045
∑y = 807246
∑(x^2) = 19142784
Now, substitute these values into the slope formula:
slope = (4 * 1416865588 - 10045 * 807246) / (4 * 19142784 - 10045^2)
slope ≈ 140.003
Next, to find the y-intercept, we can use the formula:
y-intercept = (∑y - slope * ∑x) / n
y-intercept = (807246 - 140.003 * 10045) / 4
y-intercept ≈ -15632.243
Therefore, the linear regression equation is:
Selling Price ≈ 140.003 * Square Feet - 15632.243