Question

Use the given data to find the equation of the regression line. Examine the scatterplot and identify a characteristic of the data that is ignored by the regression line. x 10 15 y 14.08 14.64 5 4.64 14 15.24 11 14.90 12 8 9 15.36 11.36 12.90 7 9.48 6 13 7.24 15.48 y=+(Round to two decimal places as needed.)
b. What is the equation of the regression line for the set of ​points?

The best predicted weight for a bear with a chest size of 48 inches is .......nothing pounds.

The best predicted temperature when a bug is chirping at 3000 chirps per minute is .........F.

Answer 1

1)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	110.00	135.32	110.00	137.0	110.00
mean	10.00	12.30	SSxx	SSyy	SSxy

Sample size,   n =   11      
here, x̅ = Σx / n=   10.000          
ȳ = Σy/n =   12.302          
SSxx =    Σ(x-x̅)² =    110.0000      
SSxy=   Σ(x-x̅)(y-ȳ) =   110.0      
              
estimated slope , ß1 = SSxy/SSxx =   110/110=   1.0000      
intercept,ß0 = y̅-ß1* x̄ =   12.3018- (1 )*10=   2.3018      
              
Regression line is, Ŷ=   2.30 + (   1.00 )*x
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2)

using all ten points

a)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	56.00	44.00	20.40	20.4	-14.40
mean	5.60	4.40	SSxx	SSyy	SSxy

Sample size,   n =   10      
here, x̅ = Σx / n=   5.600          
ȳ = Σy/n =   4.400          
SSxx =    Σ(x-x̅)² =    20.4000      
SSxy=   Σ(x-x̅)(y-ȳ) =   -14.4      
              
estimated slope , ß1 = SSxy/SSxx =   -14.4/20.4=   -0.7059      
intercept,ß0 = y̅-ß1* x̄ =   4.4- (-0.7059 )*5.6=   8.3529      
              
Regression line is, Ŷ=   8.353   + (   -0.706   )*x

b) after removing point (2,8)

Regression line is, Ŷ=   4.000   + (   0.000   )*x
=======================

3)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	311.00	1724.00	222.83	24591.3	2282.33
mean	51.83	287.33	SSxx	SSyy	SSxy

Sample size,   n =   6      
here, x̅ = Σx / n=   51.833          
ȳ = Σy/n =   287.333          
SSxx =    Σ(x-x̅)² =    222.8333      
SSxy=   Σ(x-x̅)(y-ȳ) =   2282.3      
              
estimated slope , ß1 = SSxy/SSxx =   2282.3333/222.8333=   10.2423      
intercept,ß0 = y̅-ß1* x̄ =   287.3333- (10.2423 )*51.8333=   -243.5610      
              
Regression line is, Ŷ=   -243.6 + (   10.2 )*x

Predicted Y at X=   48   is          
Ŷ=   -243.56096   +   10.24233   *48=   248.1

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4)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	5615.00	462.90	132398.83	671.4	9082.75
mean	935.83	77.15	SSxx	SSyy	SSxy

Sample size,   n =   6      
here, x̅ = Σx / n=   935.833          
ȳ = Σy/n =   77.150          
SSxx =    Σ(x-x̅)² =    132398.8333      
SSxy=   Σ(x-x̅)(y-ȳ) =   9082.8      
              
estimated slope , ß1 = SSxy/SSxx =   9082.75/132398.8333=   0.0686      
intercept,ß0 = y̅-ß1* x̄ =   77.15- (0.0686 )*935.8333=   12.9505      
              
Regression line is, Ŷ=   12.95 + (   0.0686 )*x