Solved: A manufacturing firm has developed a skills test, the scores from

A manufacturing firm has developed a skills test, the scores from which can be used to predict workers’ production rating factors. Click the icon to view the data on the test scores of various workers and their subsequent production ratings. a. Using POM for Windows’ least squares-linear regression module, develop a relationship to forecast production ratings from test scores. (Round your responses to three decimal places and include a minus sign if necessary.) Y = 1.672 + 0.942 X where Y = Production rating and X = Test score. b. If a worker’s test score was 93, what would be your forecast of the worker’s production rating? 89. (Enter your response as an integer.) c. Comment on the strength of the relationship between the test scores and production ratings. The coefficient of correlation for the least-squares regression model is and the coefficient of determination is. (Enter your responses rounded to three decimal places.)

Expert Answer

Worker	Test Score (x)	Production rating (y)	x^2	xy	y^2
A	51	40	2601	2040	1600
B	34	38	1156	1292	1444
C	87	84	7569	7308	7056
D	82	74	6724	6068	5476
E	84	79	7056	6636	6241
F	62	65	3844	4030	4225
G	48	44	2304	2112	1936
H	46	43	2116	1978	1849
I	37	39	1369	1443	1521
J	65	71	4225	4615	5041
K	52	54	2704	2808	2916
L	71	72	5041	5112	5184
M	63	56	3969	3528	3136
N	27	23	729	621	529
O	50	46	2500	2300	2116
P	20	22	400	440	484
Q	74	72	5476	5328	5184
R	30	29	900	870	841
S	43	55	1849	2365	3025
T	35	27	1225	945	729
Total	1061	1033	63757	61839	60533

Regression equation is y=a+bx

where

$a=frac{sum y*(sum x^{2})-sum x*(sum xy)}{n(sum x^{2})-(sum x)^{2}}$

$b=frac{n*(sum xy)-(sum x)*(sum y)}{n(sum x^{2})-(sum x)^{2}}$

a=(1033*63757 – 1061*61839) / (20*63757-1061²) = 1.672

b=(20*61839-1061*1033) / (20*63757-1061²)= 0.942

Thus regression equation is y=1.672+0.942x

a) y=1.672+0.942x

b) when worker test score is 93 that is x=93, the production rating is

y=1.672+0.942*93 = 89.28 = 89

c) Coefficient of correlation is given by formula

$r=frac{nsum xy-sum xsum y}{sqrt{nsum x^{2}-(sum x)^{2}}sqrt{nsum y^{2}-(sum y)^{2}}}$

r=(20*61839-1061*1033)/[(20*63757-1061²)^1/2 * (20*60533-1033²)^1/2] = 0.96

r measures the strength and direction of linearb relationship. Value of greater than 0.8 indicates strong relation ship. Thus test score and production rating have strong and positive relationship

Coefficient of determination is r² .

Thus Coefficient of determination = 0.96² = 0.9216

It gives proportion of variation in one variable prdictable by other. Thus 92.14% variation in Production rating can be predicted by test score. The remaining 7.86% is unexplained

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