Question

3. World truck production (fictional) ON HTAM Year x 1984 1985 1986 1987 1988 15.9 16.3 16.8 17.2 17.5 Trucks y (millions) a) Construct a scatterplot (show the rough graph) 1984 1915 lane 1987 1988 b) Find the correlation coefficient c) Find the formula for the regression line

Answer 1

a)

Trucks(millions) vs Year 17.5 17.0 у 16.5 16.0 1984 1985 1986 1987 1988 х

b)

Note that,

2. Σ(Ti - )(yi - g) Στι )2Σ(yi y)2

Serial no.	C	$y_i$	$(x_i-\bar x)^2$	$(y_i-\bar y)^2$	$(x_i-\bar x)(y_i-\bar y)$
1	1984	15.9	4	0.7056	1.68
2	1985	16.3	1	0.1936	0.44
3	1986	16.8	0	0.0036	0
4	1987	17.2	1	0.2116	0.46
5	1988	17.5	4	0.5776	1.52
Total	9930	83.7	10	1.692	4.1
mean	1986	16.74

From the table of calculations above we have

$r^2 =\frac{4.1}{\sqrt{10*1.692}}=0.9967 \Rightarrow r = 0.9983$

c) The equation of the least square regression is : Y= a+bX

where the least square estimates are as follows, $\hat b=\frac{\sum(x_i-\bar x)(y_i-\bar y)}{\sum(x_i-\bar x)^2}=\frac{4.1}{10}=0.41$

$\hat a=\bar y - \hat b\bar x = 16.74 - (0.41)*1986=-797.52$

Hence ,

Y = -797.52 + 0.41 X is the required equation.