Linear Regression
Essay by RAVI shankar • November 28, 2016 • Course Note • 468 Words (2 Pages) • 1,203 Views
Simple Linear Regression
Reression
Problems with Solutions

Q1. The values of y and their corresponding values of y are shown in the table below
X  0  1  2  3  4 
Y  2  3  5  4  6 
a) Find the least square regression line y = ax + b.
b) Estimate the value of y when x = 10.
Answer:
a) We use a table to calculate a and b.
x  y  x y  x 2 
0  2  0  0 
1  3  3  1 
2  5  10  4 
3  4  12  9 
4  6  24  16 
Σx = 10  Σy = 20  Σx y = 49  Σx2 = 30 
We now calculate a and b using the least square regression formulas for a and b.
a = (nΣx y  ΣxΣy) / (nΣx2  (Σx)2) = (5*49  10*20) / (5*30  102) = 0.9
b = (1/n)(Σy  a Σx) = (1/5)(20  0.9*10) = 2.2
b) Now that we have the least square regression line y = 0.9 x + 2.2, substitute x by 10 to find the value of the corresponding y.
y = 0.9 * 10 + 2.2 = 11.2
Q2. The sales of a company (in million dollars) for each year are shown in the table below.
x (year)  2005  2006  2007  2008  2009 
y (sales)  12  19  29  37  45 
a) Find the least square regression line y = ax + b.
b) Use the least squares regression line as a model to estimate the sales of the company in 2012.
Answer:
a) We first change the variable x into t such that t = x  2005 and therefore t represents the number of years after 2005. Using t instead of x makes the numbers smaller and therefore managable. The table of values becomes.
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