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## Econometrics Assignment

. Estimate the values of β0 andβ1

Y1= β0+ β1X1+u1

Where Y1 is the dependent variable

X is the independent variable

β0 is the y intercept (the value of Y when X is zero)

β1 is the slope of the line

u1 is the residual or error term

β1= N (∑XY)-(∑X) (∑Y)/N (∑X2)- (∑X)2

β1= 10(4485) -(155) (278)/10(2453) -(155)2

β1 = 44850-43090/ 24530-24025

β1 = 1760/505

β1 = 3.49

β0 = My – β1Mx

β0 = 27.8- (15.5×3.49)

β0 = 27.8-54.095

β0 = -26.30

2. Calculate the error u1 for all the observations made

Y1 = -26.30+ 3.49X1+u1

1st observation

Replace the y and x values in the equation

22 = -26.30+ (3.49×12) + u1

22 = 15.58+ u1

U1 = 6.42

2nd Observation

38 = -26.30+(3.49×17) + u1

38 = 33.03+u1

U1 = 4.97

3rd Observation

31 = -26.30+ (3.49×16) + u1

31 = 29.54+ u1

U1= 1.46

4th Observation

15 = -26.30 + (3.49x 13) + u1

U1 = -4.07

5th Observation

20 = -26.30+ (3.49×16) + u1

U1 = -9.54

6th Observation

27 = -26.30+ (3.49×17) + u1

U1 = -6.03

7th Observation

41 = -26.30+ (3.49×19) + u1

U1 = 0.99

8th Observation

22 = -26.30+ (3.49×14) + u1

U1 = -0.56

9th Observation

43 = -26.30+ (3.49×18) + u1

U1 = 6.48

10th Observation

19 = -26.30+ (3.49×13) + u1

U1 = -0.07

Summary of the error values

 Observations Error (u1) (u1)2 Deviation from mean (Deviation)2 1 6.42 41.22 3.69 13.62 2 4.97 24.70 2.24 5.02 3 1.46 2.13 -1.27 1.61 4 4.07 16.56 1.34 1.80 5 9.54 91.01 6.81 46.38 6 -6.03 36.36 -8.76 76.74 7 0.99 0.98 -1.74 3.03 8 -0.56 0.31 -3.29 10.82 9 6.48 41.99 3.75 14.06 10 -0.07 0.00 -2.8 7.84 Mean 2.73 Sum 255.26 180.92

3. Calculate and interpret the standard error of regression

The formula for calculating the regression error is Standard Error = √Sum of error squared/number of observations

The error values give the distance between the actual data points and the regression line. The regression error evaluates the precise nature of the model in predictions based on the dependent variable units. A smaller value of the standard error signifies a lower distance between the regression line and the data points and is therefore desired. A smaller value indicates that the model is sufficiently precise.

The standard error of regression for the sample is calculated below

Standard Error = 5.05

The value obtained is relatively high, thus it can be concluded that the model is not highly sufficient in making the predictions.

4. Calculate and interpret the standard error for B1

Standard Error = 1.10

5. Test the null hypothesis H0:B1=0 (p=0.05)

Test statistics = x-µ/SD/√n

SD = 9.43

Test Statistics = (27.8-0)/(9.43/3.16)

Test Statistics = 9.32

The z score falls outside the range, justifying the rejection of the null hypothesis.

Therefore, there is no sufficient evidence to accept the hull hypothesis