Year: 1990,1992, 1994, 1996, 1998, 2000, 2002, 2004, 2006

Question

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​).

Answer 1

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)

Answer 2

try again

Answer 3

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

Answer 4

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.)

Answer 5

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.

Answer 6

no

Answer 7

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.

Answer 8

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.)

Answer 9

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

Answer 10

rewrite

Answer 11

Apologies for the confusion. Let's rewrite the linear regression equation.

Based on the given data points:

Square Feet: 1511, 2512, 3007, 3015
Selling Price: $93,246, $229,000, $250,000, $265,000

The linear regression equation is:

Selling Price ≈ 140.003 * Square Feet - 15632.243

This equation estimates the selling price based on the square footage of a property.