Answer:
c. y? =+4.198 x
Step-by-step explanation:
Hello!
Using the given data you need to estimate the equation of linear regression.
Dependent variable:
Y: Annual percentage change in stock price for a company.
Independent variable:
X: Annual percentage change in profits for the company.
The population regression line equation is:
[tex]Y_i= \alpha + \beta X_i + E_i[/tex]
To estimate the equation you need to find the point estimator for α and β.
The following formulas are the ones to use:
α ⇒ a= y[bar] - bX[bar]
β ⇒ b= (∑xy - [(∑x)(∑y)]/n)/(∑X²-(∑x)²/n)
As you can see you need to make several summatories before calculating the values of a and b:
n= 7
∑x= 36.30
∑x²= 667.09
∑y= 51.60
∑y²= 747.98
∑xy= 560.74
Sample mean of de dependent variable Y[bar]= ∑y/n= (51.60/7)= 7.37
Sample mean of the independent variable X[bar]= ∑x/n= (36.30/7)= 5.19
b= [tex]\frac{560.74-\frac{(36.3*51.6)}{7} }{667.09-\frac{(51.60)^2}{7} }[/tex]
b= 0.6122
a= [tex]7.37-(0.61*5.19)[/tex]
a= 4.196
The estimated regression equation is:
Y= 4.196 + 0.6122x
I hope it helps!
