Golden Years Easy Retirement Homes owns several adult care facilities throughout the southeast United States. A budget analyst for Golden Years has collected the data found in the file “Data of Golden Years Retirement Homes – see below” describing for each facility: the number of beds(X1), annual number of medical in-patient days(X2), and the total annual patient days (X3). If the budget analyst wanted to build the best regression model, what variables should be used? Based on this analysis, which facility should the budget analyst be concerned about?
Correlation
Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.
Linear Correlation
A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.
Regression Analysis
Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.
Golden Years Easy Retirement Homes owns several adult care facilities throughout the southeast United States. A budget analyst for Golden Years has collected the data found in the file “Data of Golden Years Retirement Homes – see below” describing for each facility: the number of beds(X1), annual number of medical in-patient days(X2), and the total annual patient days (X3).
- If the budget analyst wanted to build the best regression model, what variables should be used?
- Based on this analysis, which facility should the budget analyst be concerned about?
X1 |
X2 |
X3 |
Y |
|
|
|
Number of beds in home |
Annual medical in-patient days (100s) |
Annual total patient days (100s) |
(Y) Annual nursing salaries ($100s) |
Forecast (Y^) using TREND |
Forecast (Y^) |
Y-Y^ |
137 |
128 |
385 |
5230 |
6557.04 |
6557.04 |
-1327.04 |
59 |
155 |
203 |
2459 |
2666.70 |
2666.70 |
-207.70 |
120 |
281 |
392 |
6304 |
5328.81 |
5328.81 |
975.19 |
120 |
291 |
419 |
6590 |
5684.71 |
5684.71 |
905.29 |
120 |
238 |
363 |
5362 |
5193.89 |
5193.89 |
168.11 |
65 |
180 |
234 |
3622 |
3030.71 |
3030.71 |
591.29 |
120 |
306 |
372 |
4406 |
4816.70 |
4816.70 |
-410.70 |
90 |
214 |
305 |
4173 |
4153.51 |
4153.51 |
19.49 |
96 |
155 |
169 |
1955 |
2486.02 |
2486.02 |
-531.02 |
120 |
133 |
188 |
3224 |
3195.24 |
3195.24 |
28.76 |
62 |
148 |
192 |
2409 |
2573.66 |
2573.66 |
-164.66 |
120 |
274 |
300 |
2066 |
3908.52 |
3908.52 |
-1842.52 |
116 |
154 |
321 |
5946 |
5125.70 |
5125.70 |
820.30 |
59 |
120 |
164 |
1925 |
2310.23 |
2310.23 |
-385.23 |
80 |
261 |
284 |
4166 |
3358.30 |
3358.30 |
807.70 |
120 |
338 |
375 |
5257 |
4619.41 |
4619.41 |
637.59 |
80 |
77 |
133 |
1988 |
2349.88 |
2349.88 |
-361.88 |
100 |
204 |
318 |
4156 |
4536.85 |
4536.85 |
-380.85 |
60 |
97 |
213 |
1914 |
3281.47 |
3281.47 |
-1367.47 |
110 |
178 |
280 |
5173 |
4225.78 |
4225.78 |
947.22 |
120 |
232 |
336 |
4630 |
4807.32 |
4807.32 |
-177.32 |
135 |
316 |
442 |
7489 |
6009.10 |
6009.10 |
1479.90 |
59 |
163 |
191 |
2051 |
2413.11 |
2413.11 |
-362.11 |
60 |
96 |
202 |
3803 |
3112.90 |
3112.90 |
690.10 |
25 |
74 |
83 |
2008 |
1030.68 |
1030.68 |
977.32 |
75 |
225 |
250 |
1288 |
3040.41 |
3040.41 |
-1752.41 |
64 |
91 |
214 |
4729 |
3382.85 |
3382.85 |
1346.15 |
62 |
146 |
204 |
2367 |
2781.25 |
2781.25 |
-414.25 |
108 |
255 |
366 |
5933 |
4993.54 |
4993.54 |
939.46 |
62 |
144 |
220 |
2782 |
3052.92 |
3052.92 |
-270.92 |
90 |
151 |
286 |
4651 |
4332.15 |
4332.15 |
318.85 |
146 |
100 |
375 |
6857 |
6700.06 |
6700.06 |
156.94 |
62 |
174 |
189 |
2143 |
2326.24 |
2326.24 |
-183.24 |
30 |
54 |
88 |
3025 |
1313.33 |
1313.33 |
1711.67 |
79 |
213 |
278 |
2905 |
3620.37 |
3620.37 |
-715.37 |
44 |
127 |
158 |
1498 |
2012.85 |
2012.85 |
-514.85 |
120 |
208 |
423 |
6236 |
6385.19 |
6385.19 |
-149.19 |
100 |
255 |
300 |
3547 |
3857.42 |
3857.42 |
-310.42 |
49 |
110 |
177 |
2810 |
2496.79 |
2496.79 |
313.21 |
123 |
208 |
336 |
6059 |
5020.85 |
5020.85 |
1038.15 |
82 |
114 |
136 |
1995 |
2133.93 |
2133.93 |
-138.93 |
58 |
166 |
205 |
2245 |
2604.57 |
2604.57 |
-359.57 |
110 |
228 |
323 |
4029 |
4531.32 |
4531.32 |
-502.32 |
62 |
183 |
222 |
2784 |
2785.94 |
2785.94 |
-1.94 |
86 |
62 |
200 |
3720 |
3597.36 |
3597.36 |
122.64 |
102 |
326 |
355 |
3866 |
4213.89 |
4213.89 |
-347.89 |
135 |
157 |
471 |
7485 |
7692.84 |
7692.84 |
-207.84 |
78 |
154 |
203 |
3672 |
2861.31 |
2861.31 |
810.69 |
83 |
224 |
390 |
3995 |
5369.77 |
5369.77 |
-1374.77 |
60 |
48 |
213 |
2820 |
3657.17 |
3657.17 |
-837.17 |
54 |
119 |
144 |
2088 |
1948.28 |
1948.28 |
139.72 |
120 |
217 |
327 |
4432 |
4778.14 |
4778.14 |
-346.14 |
|
|
|
|
|
|
|
|
|
b0 |
22.33121256 |
|
|
|
|
|
b1 |
9.838841555 |
|
|
|
|
|
b2 |
-7.667412573 |
|
|
|
|
|
b3 |
16.02133159 |
|
|
|
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