Question

The table below gives the average household savings per month for a city from 2006 to 2017. In this table, a represents the years since 2006 and y represents the average household savings per month in dollars. Use a TI-83, TI-83 plus, or TI-84 calculator to find the equation of the regression line. Round the slope and intercept to one decimal place. 22.73 21.44 22.56 24.05 20.68 21:22 Help Copy to Cipboard Download CSV

Answer 1

X	Y	$(y-\bar{y})^{2}$	$(x-\bar{x})^{2}$
3	23.58	3.233	16
4	23.29	2.274	9
5	23.33	2.396	4
6	24.05	5.144	1
7	20.68	1.214	0
8	21.22	0.316	1
9	20.65	1.281	4
10	19.88	3.618	9
11	19.36	5.866	16
$\sum x$ = 63	$\sum y$ = 196.04	25.342	60

$\bar{y}=\sum y/n$ =21.782 , $\bar{x}=\sum x/n$ = 7

The regression line is given by,

y = a + b x,

where,   $\hat{a}=\bar{y}-\hat{b}\bar{x}$ , and $\hat{b} = r \frac{S_{y}}{S_{x}}$

where, r is the correlation coefficient. and S_y and S_x are the standard deviation of y and x respectively.

$S_{y}=\sqrt{\sum (Y_{i}-\bar{y})^{2}/n}$

= 1.678

$S_{x}=\sqrt{\sum (x_{i}-\bar{x})^{2}/n}$

= 2.582

$r=\frac{cov(x,y)}{S_{x}*S_{y}}$

cov(x,y) = -1.14

r = -0.263

Therefore, the slope is given by, $\hat{b}$ = (-0.263)*(1.678/2.582) = -0.2

and the intercept is given by, $\hat{a}$ = 21.782 - (-0.2)*7 = 23.2

therefore, the regression equation is given by,

y = 23.2 -0.2x  

y+0.2 x = 23.2 (ans)

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