2.5 – Modeling Real World Data:. Using Scatter Plots.

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Presentation transcript:

2.5 – Modeling Real World Data:

Using Scatter Plots

Ex.1 The table below shows the median selling price of new, privately-owned, one-family houses for some recent years.

Year Price ($1000)

Ex.1 The table below shows the median selling price of new, privately-owned, one-family houses for some recent years. a.Make a scatter plot of the data. Year Price ($1000)

Years Since 1990

Price Years Since 1990

Price ($1000) Years Since 1990

Median House Prices Price ($1000) Years Since 1990

Median House Prices Price ($1000) 0 Years Since 1990

Median House Prices Price ($1000) Years Since 1990

Median House Prices Price ($1000) Years Since 1990

Median House Prices Price ($1000) Years Since 1990

Median House Prices Price ($1000) Years Since 1990

Median House Prices Price ($1000) Years Since 1990

Median House Prices Price ($1000) Years Since 1990

Median House Prices Price ($1000) Years Since 1990

Median House Prices Price ($1000) Years Since 1990

Median House Prices Price ($1000) Years Since 1990

Median House Prices Price ($1000) Years Since 1990

Median House Prices Price ($1000) Years Since 1990 b. Make a line of fit.

Median House Prices Price ($1000) Years Since 1990 b. Make a line of fit.

Median House Prices Price ($1000) Years Since 1990 b. Make a line of fit.

c.Find a prediction equation for line of fit.

*Use the best two ordered pairs from b. to find the slope for the line!

c.Find a prediction equation for line of fit. *Use the best two ordered pairs from b. to find the slope for the line! (4, 130) and (8, 152.5)

c.Find a prediction equation for line of fit. *Use the best two ordered pairs from b. to find the slope for the line! (4, 130) and (8, 152.5) m = y 2 – y 1 x 2 - x 1

c.Find a prediction equation for line of fit. *Use the best two ordered pairs from b. to find the slope for the line! (4, 130) and (8, 152.5) m = y 2 – y 1 = – 130 x 2 - x 1 8 – 4

c.Find a prediction equation for line of fit. *Use the best two ordered pairs from b. to find the slope for the line! (4, 130) and (8, 152.5) m = y 2 – y 1 = – 130 = 22.5 x 2 - x 1 8 – 4 4

c.Find a prediction equation for line of fit. *Use the best two ordered pairs from b. to find the slope for the line! (4, 130) and (8, 152.5) m = y 2 – y 1 = – 130 = 22.5 ≈ 5.63 x 2 - x 1 8 – 4 4

c.Find a prediction equation for line of fit. *Use the best two ordered pairs from b. to find the slope for the line! (4, 130) and (8, 152.5) m = y 2 – y 1 = – 130 = 22.5 ≈ 5.63 x 2 - x 1 8 – 4 4 *So use x 1 = 4

c.Find a prediction equation for line of fit. *Use the best two ordered pairs from b. to find the slope for the line! (4, 130) and (8, 152.5) m = y 2 – y 1 = – 130 = 22.5 ≈ 5.63 x 2 - x 1 8 – 4 4 *So use x 1 = 4, y 1 = 130

c.Find a prediction equation for line of fit. *Use the best two ordered pairs from b. to find the slope for the line! (4, 130) and (8, 152.5) m = y 2 – y 1 = – 130 = 22.5 ≈ 5.63 x 2 - x 1 8 – 4 4 *So use x 1 = 4, y 1 = 130, and m ≈ 5.63

c.Find a prediction equation for line of fit. *Use the best two ordered pairs from b. to find the slope for the line! (4, 130) and (8, 152.5) m = y 2 – y 1 = – 130 = 22.5 ≈ 5.63 x 2 - x 1 8 – 4 4 *So use x 1 = 4, y 1 = 130, and m ≈ 5.63 y – y 1 = m(x – x 1 )

c.Find a prediction equation for line of fit. *Use the best two ordered pairs from b. to find the slope for the line! (4, 130) and (8, 152.5) m = y 2 – y 1 = – 130 = 22.5 ≈ 5.63 x 2 - x 1 8 – 4 4 *So use x 1 = 4, y 1 = 130, and m ≈ 5.63 y – y 1 = m(x – x 1 )

c.Find a prediction equation for line of fit. *Use the best two ordered pairs from b. to find the slope for the line! (4, 130) and (8, 152.5) m = y 2 – y 1 = – 130 = 22.5 ≈ 5.63 x 2 - x 1 8 – 4 4 *So use x 1 = 4, y 1 = 130, and m ≈ 5.63 y – y 1 = m(x – x 1 ) y – 130 = 5.63(x – 4) y – 130 = 5.63(x) – 5.63(4) y – 130 = 5.63x – y = 5.63x

d.Predict the price in 2020.

2020 means when x=30 (yrs after 1990)

d.Predict the price in means when x=30 (yrs after 1990) *Plug 30 in for x!

d.Predict the price in means when x=30 (yrs after 1990) *Plug 30 in for x! y = 5.63x

d.Predict the price in means when x=30 (yrs after 1990) *Plug 30 in for x! y = 5.63x y = 5.63(30)

d.Predict the price in means when x=30 (yrs after 1990) *Plug 30 in for x! y = 5.63x y = 5.63(30) y =

d.Predict the price in means when x=30 (yrs after 1990) *Plug 30 in for x! y = 5.63x y = 5.63(30) y = y =

d.Predict the price in means when x=30 (yrs after 1990) *Plug 30 in for x! y = 5.63x y = 5.63(30) y = y = So, in 2020 the price will be $276,380.