Question

Simple Linear Regression Explain with Your Example : no need for any line drawing

1)Slope b1= Beta positive or Negative is positive ?

2)b0 is the y intercept of the line.?

3)Equation; Linear regression equation=

4)y is the estimated value of y for a given x value.

5)Coefficient of Determination
Explain If r = 0.8584t   then R to power 2 (r^2 =?) Would be ? What is it mean and interpretation of it.

Answer 1

1) slope (b1):

if slope value with negative sign,then equation is negative direction. ex. 102 - 2.3*X

and slpoe value with positive sign , then equation is positve direction ex. 102 + 2.3 *X

2)intercept(b0) :

intercept is plotted on y axis, y pred value if x equal to zero ,this is intercept.

ex. =102 + 2.3*X

= 102 + 2.3*0

=102 this is intercept

; 3) simple linear regression equation ( only one independent variable)

y hat = B0 + B1X

multiple linear regression equation:(more then two independent variable)

y hat = B0 + B1X + B2X + B3X + B4X + ........+ BnX

4) y on x regression equation

y is dependent variable and x is independent vaariable, if x values changes then y values also cheanges.

if want to new predict then pass the values of x.

5) corr= 0. 858

r square+?

r square value is directly square of correlation coefficient

r2= corr ^ 0

= 0.852 ^ 2

=0.7362

r2 = 0.7362 it ,means our model fitted 73.62% correctly, r2 lies between 0 to 1.