Archangel Macsika
Researcher is using data for a sample of 10 observations to estimate the relation between consumption expenditure and income. Preliminary analysis of the sample data produces the following data. ∑xy = 700 , 1000 2 ∑x = , ∑X = 100 ∑Y = 200 Where i x Xi X __ = − and __ y = Yi − Y a. Use the above information to compute OLS estimates of the intercept and slope coefficients and interpret the result b. Calculate the variance of the slope parameter c. Compute the value R 2 (coefficient of determination) and interpret the result d. Compute 95% confidence interval for the slope parameter e. Test the significance of the slope parameter at 5% level of confidence using t-test
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a) Define Y^ = b0 + b1x
where b0 is the y intercept and b1 is the slope or regression coefficient of the line.
b1 = (∑xy - (∑X ∑Y)/n ) /( ∑X2 - ( ∑X )2/n )
which yields
= (700 - (100 * 200)/10) / ( 1000 - (100)2/10)
= (-1300)/ ( 0 ) which is undefined
since b1 is undefined,it makes it impossible to handle part b, c, d and e respectively.
b) variance of the slope = MSE/ ∑( XI - X- )2
c) coeeficient of determination = ( coefficient of correlation)2
d) t = b1/sb1 , where b1 is the slope and sb1 is the of the variance of the slope
e) if tcalculated > ttabulated ,then we conclude that the slope is significant.