Problem 1:

We are given a data containing one dependent variable and one independent variable. Salary is the target variable (dependent variable) and Experience in years (Explanatory variable).We are asked to estimate the parameters beta not and beta one and to arrive at a equation that Estimates the value of Salary when are given a value of experience in years.

Let y= a+bx be the regression line of y on x. The constants a and b can be found out using the following normal equations

Standard Normal Equation

  • 2280.09 = 30*a + 159.4b         … (1)
  • 14321.961 = 159.4a + 1080.5*b  ….(2)
  • 363446.346=4782a+25408.36b  …(3)
  • 429658.83 = 4782a +32415b   ….(4)
  • Deduct 3 from 4
  • 12.484 = 7006.64b 
  • b = 66212. 484/7006.64 =9.449962321
  • Substitute b in equation 1
  • 2280.09 = 30a +1080.5*66212. 484
  • 2280.09 = 30a +1506.324
  • 30a = 2280.09-1506.324 =773.766
  • a = 773.766/30 =25.7922

Equation:

  • Y hat = 25.7922 + 9.449962321X
  • Estimate the value of y when  value of X = 11
  • Yhat = 25.7922 + 9.449962321*11
  • Yhat  = 129.74