Question

A) A sample of 13 observations collected in a regression study on two variables, x(independent variable) and y(dependent variable). The sample resulted in the following data.

summation (x_i-xbar)²=14, summation (x_i-xbar)(y_i-ybar)=72,    xbar=3, ybar=10

Calculate the y-intercept (b_0) of the estimated regression equation.

B) A sample of 9 observations collected in a regression study on two variables, x(independent variable) and y(dependent variable). The sample resulted in the following data.

summation (x_i-xbar)²=14, summation (x_i-xbar)(y_i-ybar)=79,    xbar=3, ybar=10

Calculate the slope of the estimated regression equation.

Answer 1

solution: A)

the given information is as follows:

,

since Y is dependent variable

form of regression equation = Y = a + bX

where a is y intercept and b is known as slope

so regression equation of Y on X is given as follows:

pjutting the values in the above equation

=

so slope = 5.143

and y intercept = -5.429

solution B)

the given information is as follows:

,

since Y is dependent variable

form of regression equation = Y = a + bX

where a is y intercept and b is known as slope

so regression equation of Y on X is given as follows:

pjutting the values in the above equation

=

so slope = 5.643

and y intercept = -6.929