Question

Score: 0 or 3 pts 9.2.33 Use the data in the table below to complete parts (a) through (d) 11 of 15 (10 complete) 34 20 40 23 Click the icon to view details on how to construct and interpret residual plots. 43 26 59 28 53 26 21 29 28 23 뮬 (a) Find the equation of the regression line. Steps for Constructing a Residual Plot (Round to three decimal places as needed.) To construct a residual plot, make a scatter piot of (xy-), where y- is the residual of each y-value. If the resulting plot shows any type of pattern, the regression line is not a good representation of the relationship between the two variables. It it does not show a pattem, that is, the residuals fiuctuate about 0, then the regression line is a good representation. Be aware that if a point on the residual plot appears to be outside the pattern of the other points, then it may be an outlier Print Done

Answer 1

From the given data,the following statistics are calculated.

$\sum X=415$

$\bar{x}$ = 46.1111

$\sum Y=223$

$\bar{y}$ = 24.8889

x - $\bar{x}$	y - $\bar{y}$	(x - $\bar{x}$ )2	(x - $\bar{x}$ )(y - $\bar{y}$ )
- 8.1111	- 3.8889	65.7901	31.5432
- 12.1111	- 4.8889	146.679	59.2099
- 6.1111	-1.8889	37.3457	11.5432
- 0.1111	4.1111	0.0123	- 0.4568
- 3.1111	1.1111	9.679	- 3.4568
1.8889	3.1111	3.5679	5.8765
12.8889	3.1111	166.1235	40.0988
7.8889	- 1.8889	62.2346	- 14.9012
6.8889	1.1111	47.4568	7.6542
Total		SSX = 538.8889	SP = 137.1111

Sum of Squares = SS_X = 538.8889

Sum of Products = SP = 137.1111

$b=\frac{SP}{SS_{X}}=\frac{137.1111}{538.8889}=0.2544$

$a=\bar{y}-b\bar{x}$

$=24.8889-(0.2544\times 46.1111)=13.1567$

So,

Equation of the regression line is:

$\hat{y}=0.254x+13.157$