Question

1.7 Four people are allowed to pick pemies from the botom of a pol. Each f Y, dollars worth of pennies during the X, minutes the four people are allowed in the pool: Person Dollars Found, Y, 2.00 5.00 6.00 7.00 Minutes, X, (a) What is the centroid for this sample? (b) What is b, of the least squares line Y, bo + biX,? (c) What is bo of the least squares line Y, bo + bX,? (d) Interpretation: People tend to find about for each additional minute in the pool.

Answer 1

According to the question,

We need to find b₀ and b₁ of the regression line:

the formulas are :

  $b_1 = \frac{n \sum_i x_i y_i - \sum_i x_i \sum_i y_i}{n \sum_i x_i^{2}- \sum_i x_i}$

$b_0 = \bar y - b_1 \bar x$

	Y	X	XY	X^2
	2	1	2	1
	5	2	10	4
	6	3	18	9
	7	6	42	36
total	20	12	72	50

$b_1 = \frac{4*72 - 20*12}{4*50 - 12}$

$b_1 = \frac{288 - 240}{200-12} ;$

$b_1 = \frac{48}{188} ;$

$b_1 = 0.255$

$b_0 = 5- 0.255*3$$(\bar y = \frac{20}{4} = 5 ; \bar x = \frac{12}{4} =3)$

$b_0 = 5- 0.766$

$b_0 =4.234$

a) Centroid of a given sample

$mean = \frac{\sum_i x_i y_i}{\sum_i x_i}$

$mean = \frac{72}{12} =6$

b)$b_1 = 0.255$

c) $b_0 =4.234$

d)  $Y = b_0 + b_1 X$

$Y = 4.234 + 0.255* X$

People tend to find about 0.255 dollars per minute spent in a pool.