2 2 Linear Models Correlation Linear functions Y

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2. 2 Linear Models & Correlation

2. 2 Linear Models & Correlation

Linear functions Y = am x + b slope m = y 2 y

Linear functions Y = am x + b slope m = y 2 y 1 On the calculator a=m y intercept

Y = 3/4 X - 2 Y= mx + b Start at b Use

Y = 3/4 X - 2 Y= mx + b Start at b Use m for the next point 3 up 3 4 right 4

Find an equation through (1, 5) and (-2, -1). Need m and b m

Find an equation through (1, 5) and (-2, -1). Need m and b m = y 2 - y 1 m = -1 - 5 m = -6 -2 - 1 -3 x 2 - x 1 m =2

Find an equation through (1, 5) and (-2, -1). Need m and b y=

Find an equation through (1, 5) and (-2, -1). Need m and b y= mx + b y = 2 x +3 5 = 2(1) + b 5=2+b 3=b

Find an equation through (1, 5) and (-2, -1). Need m and b Shortcut

Find an equation through (1, 5) and (-2, -1). Need m and b Shortcut : Use Calculator.

Find an equation through (1, 5) and (-2, -1). Put the ordered pairs into

Find an equation through (1, 5) and (-2, -1). Put the ordered pairs into 2 Stat 1 2 -2 Edit 5 -1

Find an equation through (1, 5) and (-2, -1). Stat Calc 4: Lin Reg

Find an equation through (1, 5) and (-2, -1). Stat Calc 4: Lin Reg (ax + b) y = ax + b a=2 b=3

Direct Variation y=kx Y varies directly. k is the constant of variation.

Direct Variation y=kx Y varies directly. k is the constant of variation.

Y=kx same as y = k x

Y=kx same as y = k x

How to find k y x y = k x 2 8 8 3

How to find k y x y = k x 2 8 8 3 12 =4 2 4 16 5 20 12 = 4 3

Direct variation Goes through the origin.

Direct variation Goes through the origin.

Not direct

Not direct

Old Faithful Problem

Old Faithful Problem

Length of eruption 2. 0 2. 5 3. 0 3. 5 4. 0 4.

Length of eruption 2. 0 2. 5 3. 0 3. 5 4. 0 4. 5 Time til next eruption 57 62 68 75 83 89

2. 0 2. 5 3. 0 3. 5 4. 0 4. 5 57 62

2. 0 2. 5 3. 0 3. 5 4. 0 4. 5 57 62 68 75 83 89 80 60 40 20 0 1 2 3 4 5

Will a line connect these points? NO 80 60 40 20 0 1 2

Will a line connect these points? NO 80 60 40 20 0 1 2 3 4 5

This scatter plot has numbers close to the line. You can write an equation

This scatter plot has numbers close to the line. You can write an equation to make a prediction.

Try to fit the line through the middle of the points. Choose two points

Try to fit the line through the middle of the points. Choose two points on the line. ( , ) Find m. Find b.

Length of eruption 2. 0 2. 5 3. 0 3. 5 4. 0 4.

Length of eruption 2. 0 2. 5 3. 0 3. 5 4. 0 4. 5 Time til next eruption 57 62 68 75 83 89 Put these in a 2 lists list

Stat Calc 4: Lin Reg (ax + b) y = ax + b y

Stat Calc 4: Lin Reg (ax + b) y = ax + b y = 13. 1 X + 29. 6 a = 13. 1 correlation coefficient b = 29. 6 2 r =. 995 r =. 9976

Stat Calc 4: Lin Reg (ax + b) y = ax + b To

Stat Calc 4: Lin Reg (ax + b) y = ax + b To turn r on, go a = 13. 1 Catalogue b = 29. 6 Diagnostic On 2 r =. 995 r =. 9976

The correlation coefficient tells you how strong the line relation is. Are the dots

The correlation coefficient tells you how strong the line relation is. Are the dots in the scatter close to the line, or far awa

The correlation coefficient between -1 and +1. -1 < r < 1

The correlation coefficient between -1 and +1. -1 < r < 1

r=1 r =. 6 r=0 + slope on weaker + no the line correlation

r=1 r =. 6 r=0 + slope on weaker + no the line correlation corre

: : : r = -1 - slope on the line r = -.

: : : r = -1 - slope on the line r = -. 6 r=0 weaker no correlation corre

Linear relation strong l -1 strong + no correlation weak + l 0 Value

Linear relation strong l -1 strong + no correlation weak + l 0 Value of r

In our Old Faithful problem y = ax + b a = 13. 1

In our Old Faithful problem y = ax + b a = 13. 1 b = 29. 6 2 r =. 995 r =. 9976 What does tha tell you?

Aspire to climb as high as you can dream.

Aspire to climb as high as you can dream.