Question

A random sample of 9 history students produced the following data,

first test score, x	second test score, y
90	51
36	82
13	15
71	77
82	10
20	18
92	35
53	49
63	85

where x measures the first test score and y measures the second test score. What is the estimate of the y = a x + b regression slope coefficient?

Answer 1

Here,

X	Y
90	51
36	82
13	15
71	77
82	10
20	18
92	35
53	49
63	85

From the data, we have,

n = 9, cy = 25556, T = 57.7778, y = 46.8889, x2 = 36972

The regression slope is given by:

$a=\frac{\sum xy-n\overline{x}.\overline{y}}{\sum x^2-n\overline{x}^2} =\frac{25556-9(57.7778)(46.8889)}{36792-9(57.7778)^2}=0.17395$