Question

Run a regression analysis on the following data set, where y is the final grade in a math class and x is the average number of hours the student spent working on math each week. hours/week Grade х у 4 41.6 4 54.6 8 68.2 8 73.2 8 66.2 11 63.4 11 70.4 11 80.4 13 71.2 16 85.4 State the regression equation y = mx + b, with constants accurate to two decimal places. What is the predicted value for the final grade when a student spends an average of 12 hours each week on math? Grade = Round to 1 decimal place.

Answer 1

a)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	94.00	674.60	128.40	1397.60	352.56
mean	9.40	67.46	SSxx	SSyy	SSxy

Sample size,   n =   10      
here, x̅ = Σx / n=   9.400          
ȳ = Σy/n =   67.460          
SSxx =    Σ(x-x̅)² =    128.4000      
SSxy=   Σ(x-x̅)(y-ȳ) =   352.6      
              
estimated slope , ß1 = SSxy/SSxx =   352.56/128.4=   2.7458      
intercept,ß0 = y̅-ß1* x̄ =   67.46- (2.7458 )*9.4=   41.6495      
              
Regression line is, Ŷ=   41.6   + (   2.75 )*x

b)

Predicted Y at X=   12   is          
Ŷ=   41.64953   +   2.74579   *12=   74.6

-----------------------------

a)

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	359.00	150.00	1938.83	137.76	-22.20
mean	59.83	25.00	SSxx	SSyy	SSxy

Sample size,   n =   6      
here, x̅ = Σx / n=   59.833          
ȳ = Σy/n =   25.000          
SSxx =    Σ(x-x̅)² =    1938.8333      
SSxy=   Σ(x-x̅)(y-ȳ) =   -22.2      
              
estimated slope , ß1 = SSxy/SSxx =   -22.2/1938.8333=   -0.0115      
intercept,ß0 = y̅-ß1* x̄ =   25- (-0.0115 )*59.8333=   25.6851      
              
Regression line is, Ŷ=   25.7   + (   -0.011   )*x
              
SSE=   (SSxx * SSyy - SS²xy)/SSxx =    137.5058      
std error ,Se =    √(SSE/(n-2)) =    5.8631      
              
correlation coefficient ,    r = SSxy/√(SSx.SSy) =   -0.043

b)

Regression line is, Ŷ=   25.6851 + (   -0.0115 )*x

c)

Predicted Y at X=   62   is          
Ŷ=   25.68510   +   -0.01145   *62=   24.975

d)

x	y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)	Ŷ	residual,ei=y-y^
62	20.5	4.6944	20.2500	-9.750	24.98	-4.4752

Please let me know in case of any doubt.

Thanks in advance!

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