MTH-416, REGRESSION ANALYSIS Lecture Notes - Lecture 59: Maxima And Minima, Bias Of An Estimator, Partial Derivative

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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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Instead of minimizing the distance, the area can also be minimized. The reduced major axis regression method minimizes the sum of the areas of rectangles defined between the observed data points and the nearest point on the line in the scatter diagram to obtain the estimates of regression coefficients. No assumption is required about the form of the probability distribution of. For the purpose of deriving the statistical inferences only, we assume that variable with. This assumption is j needed to find the mean, variance and other properties of the least-squares estimates. "i s are normally distributed is utilized while constructing the tests of hypotheses and confidence intervals of the parameters. Among them, the direct regression approach is more popular. Generally, the direct regression estimates are referred to as the least-squares estimates or ordinary least squares estimates. Regression analysis | chapter 2 | simple linear regression analysis | shalabh, iit kanpur and .

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EXPLORING CONCEPTS

Method of Least Squares

Find a system of equations whose solution yields the coefficients , , and for the least squares regression quadratic

for the points by minimizing the sum

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 59: Maxima And Minima, Bias Of An Estimator, Partial Derivative

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