MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 16: Linear Regression, Confidence Interval, Bias Of An Estimator

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rosi10agarwal

6 Apr 2023

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Indian Institute of Technology - IIT Kanpur

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Mathematics

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MTH-416, REGRESSION ANALYSIS

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Application of ols fails in case of autocorrelation in the data and leads to serious consequences as. Usual t -ratio and f ratio tests provide misleading results. Since disturbances are nonspherical, so generalized least squares estimate of yields more efficient estimates than olse. The glse is best linear unbiased estimator of . The durbin-watson (d-w) test is used for testing the hypothesis of lack of the first-order autocorrelation in the disturbance term. Use ols to estimate in y x. 2(1 r r where r is the sample autocorrelation coefficient from residuals based on olse and can be regarded as the regression coefficient of. Here te on positive autocorrelation of negative autocorrelation of. 2d te "s te "s d . So r if 1 if 0 r. ,x so for different data sets, different values of d are obtained. Since e depends on distribution of d depends on x .

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Age (years) 1 2 4 10 9 8 6 3
Car’s Value ($000) 24 21 15 4 6 7 10 17
a. Compute the Coefficient of correlation. Explain the value
b. Compute the Coefficient of determination. Explain the value
c. Estimate the least square linear equation.

moneygetta

Average price per square foot of floor area in new one-family houses sold. Price per square foot of floor area excludes value of improved lot Source: Year 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 Price per square foot $55.18 $57.41 $60.21 $62.45 $64.38 $66.81 $67.83 $67.70 $70.43 $71.93 $75.68 $79.21 $85.13 $90.63 $91.99 Instead of working on portions of the scatter plots, we want to approximate the data by a line we can use to predict prices in the future. The line that will best fit the given data is called the linear regression. The approximation will be acceptable whether the determina- tion coefficient R (r**2) is close to 1 or the correlation coefficient r is close to -1 or +1.

a) using your entered data to find the equation y = ax + b of the best line through the data points and give the values of coefficients a and b, and of the determination coefficient R or correlation coefficient r.

b. Use Excel to plot the scatter plot and the regression line on the same graph.

c. Is the linear regression a visually good approximation of the data? Sustain your argument by a mathematical proof.

d. use the linear regression to predict the price per square foot area in 2009 e. In what year will the price per square foot be greater than $199?

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MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 16: Linear Regression, Confidence Interval, Bias Of An Estimator

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