# Exercise 4 Multiple Linear Regression For Exercise 4, you are going to undertake data analysis using the multiple linear regression analytical tool. You c

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Multiple Linear Regression

For Exercise 4, you are going to undertake data analysis using the multiple linear regression analytical tool. You can use the tool in any Analysis ToolPak or R (RStudio). In this instance, the analysis you are going to undertake will be slightly different depending on whether you are using an Analysis ToolPak or R. But irrespective of which tool you use you will start by setting up your data and preparing it for Regression Analysis.

Please set up your data set for regression analysis this way:

Select the columns (variables) of data that you need for all your regression runs. Create new columns (variables) of data by calculating and copying the cells. Copy all the columns (variables) of data that you need for all your regression runs to a new worksheet. Please clean up your data set for regression analysis by eliminating any data rows with missing values (or imputing the missing values) before you run the Regression to avoid errors. (The Medicare and Medicaid Discharge ratio variables have a few Division by Zero values. Any data rows with these and any other missing values need to be deleted. Save the data as a CSV file in an appropriate folder.

I have sent everyone an email message with 2 attachments with additional guidance on how to set up the data and do the regression analysis to estimate Model 1. The other models may be done in a similar fashion.

Using an Analysis ToolPak:

Model 1:

Run a multiple linear regression model to explain/predict Net Hospital Benefits (Net Revenue). The dependent variable is Net Hospital Benefits and the independent or predictor variables are Total Hospital Beds and whether the hospital is a Teaching Hospital or not. Complete Table 1.

Table 1-Model 1-To explain/predict Net Hospital Benefits – 2011, 2012

(using an Analysis Tool Pak)

Coef.

ST. ERR

T Stat

P-values

Lower 95%

Upper 95%

Intercept

Total Hospital beds

Teaching Hospital Dummy

R Square=

Model 2:

Run a multiple linear regression model and explain/predict Net Hospital Benefits (Net Revenue). In the 2nd model, the dependent variable is Net Hospital Benefits and the independent or predictor variables are Total Hospital Beds and whether the hospital is a Non-Teaching Hospital or not. (Note: You may convert the Teaching Hospital column into a Non-Teaching Hospital column by subtracting 1 and changing the sign of the data.) Complete Table 2.

Table 2-Model 2-To explain/predict Net Hospital Benefits – 2011, 2012

(using Excel Analysis Tool Pak)

Coef.

ST. ERR

T Stat

P-values

Lower 95%

Upper 95%

Intercept

Total Hospital beds

Non-Teaching Hospital Dummy

R Square=

Use the results from model 1 and model 2 to compare the results between teaching and non-teaching hospitals.

Model 3:

Run a multiple linear regression model and explain/predict Net Hospital Benefits (Net Revenue). In the 3rd model, the dependent variable is Net Hospital Benefits and the independent or predictor variables are Total Hospital Beds, whether the hospital is a Teaching Hospital or not, Ratio of Medicare Discharges, and Ratio of Medicaid Discharges. Complete Table 3.

Table 3-Model 3-To explain/predict Net Hospital Benefits – 2011, 2012

(using an Analysis Tool Pak)

Coef.

ST. ERR

T Stat

P-values

Lower 95%

Upper 95%

Intercept

Total Hospital beds

Teaching Hospital Dummy

Ratio of Medicare discharges

Ratio of Medicaid discharges

R Square=

How do you evaluate the impact of having higher or more Medicare and Medicaid patients on hospital net-benefit in teaching hospitals?

Model 4:

Run a multiple linear regression model and explain/predict Net Hospital Benefits (Net Revenue). In the 4th model, the dependent variable is Net Hospital Benefits and the independent or predictor variables are Total Hospital Beds, whether the hospital is a Non-Teaching Hospital or not, Ratio of Medicare Discharges, and Ratio of Medicaid Discharges. Complete Table 4.

Table 4-Model 4-To explain/predict Net Hospital Benefits – 2011, 2012

(using an Analysis Tool Pak)

Coef.

ST. ERR

T Stat

P-values

Lower 95%

Upper 95%

Intercept

Total Hospital beds

Non-Teaching Hospital Dummy

Ratio of Medicare discharges

Ratio of Medicaid discharges

R-Squared =

How do you evaluate the impact of having higher or more Medicare and Medicaid patients on hospital net-benefit in non-teaching hospitals?

Based on your finding please recommend 3 policies to improve hospital performance. Please make sure to use the final model for your recommendation.

Make sure to include or attach any plotted graphs that help you make your points.

Using R through RStudio:

Model 1:

Run a multiple linear regression model to explain/predict Net Hospital Benefits (Net Revenue). The dependent variable is Net Hospital Benefits and the independent or predictor variables are Total Hospital Beds, Whether Hospital is for-profit or not (dummy variable), Whether Hospital is not-for-profit or not (dummy variable), Whether Hospital is some other ownership status or not (dummy variable). Note: This is Model 1A in the R script. Complete Table 1.

Table 1-Model 1-To explain/predict Net Hospital Benefits – 2011, 2012

(using R through RStudio)

CoefficientStandard Error

T-Value

Pr(>|t|)

Intercept

Hospital beds

For-Profit Dummy

Public Ownership Dummy

Other Owner Type Dummy

R-Squared=

Discuss your findings.

Do you think having more beds has a positive impact on the hospital’s net benefit?

What about the ownership?

Note: We are not running the regression Model 1B. The model that uses the newly created bed categorical variable.

Model 2:

Now, run a multiple linear regression model to explain/predict Net Hospital Benefits (Net Revenue) as you did in Model 1, but this time add whether the hospital is a member of a system as an additional independent variable. Complete Table 2

Table 2-Model 2-To explain/predict Net Hospital Benefits – 2011, 2012

(using R through RStudio)

Coefficient

Standard Error

T-Value

Pr(>|t|)

Intercept

Hospital beds

For-Profit Dummy

Non-for-profit Dummy

Other Owner Type Dummy

System Membership

R-Squared=

Discuss your findings (not more than 2 lines).

Is the result statistically significant? Explain your answer.

Model 3:

Now, run a multiple linear regression model to explain/predict Net Hospital Benefits (Net Revenue) as you did in Model 2 above, but this time add the Medicare-discharge-ratio and Medicaid-discharge-ratio as additional independent variables. Complete Table 3.

Table 3-Model 3-To explain/predict Net Hospital Benefits – 2011, 2012

(using R through RStudio)

CoefficientStandard Error

T-Value

Pr(>|t|)

Intercept

Hospital beds

For-Profit Dummy

Non-for-profit Dummy

Other Dummy

System Membership

Medicare discharge ratio

Medicaid discharge ratio

R-Squared=

Discuss your findings (not more than 2 lines). Is the result statistically significant? Explain your answer.

Based on your findings please recommend 3 policies to improve hospital performance. Please make sure to use the final model for your recommendation.

Make sure to include or attach any plotted graphs that help you make your points.

stata_name stcd year total_hosp_cost total_hosp_revenue hospital_beds bedsize_cat teaching_hospital system_member level_trauma white rural_area herf_cat herf_index non_white log_hosp_cost log_hosp_revenue total_hospital_beds total_hospital_medicare_days total_hospital_medicaid_days interns_and_residents total_hospital_employees_on_payr total_hospital_non_paid_workers total_hospital_medicare_discharg total_hospital_medicaid_discharg total_hospital_discharges own
Arizona 86 2012 1.89E+07 1.73E+07 19 1 0 0 0 58.7 0 1 0 41.3 16.75435 16.66785 168.92 11551.5 8206.92 855.048 2695.488 2867 8879 0
Arizona 86 2012 8.01E+07 7.94E+07 88 3 0 0 0 58.5 0 1 2 41.5 18.19875 18.19 138.02 14629.86 2423.52 1209.024 4117.736 697 6998 1
Arizona 86 2012 1.47E+08 1.33E+08 134 4 0 0 0 82 0 1 2 18 18.80468 18.70265 74.16 3784.2 4354.38 490.464 1305.488 1253 4320 0
Arizona 86 2012 7.74E+07 8.81E+07 72 3 0 0 0 82 0 1 2 18 18.16424 18.29439 25.75 306 225.42 132.84 74.504 66 257 0
Arizona 86 2012 1.53E+08 1.41E+08 187 4 0 0 0 58.7 0 1 2 41.3 18.84588 18.76257 19.57 1545.3 98.94 139.608 259.096 18 429 2
Arizona 86 2012 1.60E+07 1.70E+07 21 1 0 0 0 20.4 1 0 2 79.6 16.58738 16.65044 20.6 1042.44 235.62 185.148 160.128 77 366 2
Arizona 86 2012 7.02E+08 7.55E+08 460 7 0 0 1 55.3 0 1 2 44.7 20.36947 20.4425 493.37 28329.48 46840.44 356.34 4570.98 5216.392 9139 26341 2
Arizona 86 2012 2.07E+07 2.29E+07 14 1 0 0 3 58.5 0 1 2 41.5 16.84361 16.94799 237.93 5724.24 11063.94 95.39 1073.82 1195.4 1481 6836 0
Arizona 86 2012 1.67E+08 1.72E+08 163 4 0 0 3 55.3 0 1 2 44.7 18.93446 18.96016 14.42 961.86 255 154.62 151.232 98 356 1
Arizona 86 2012 2.32E+07 2.06E+07 56 3 0 1 0 16 0 1 2 84 16.95965 16.84255 61.8 3816.84 1180.14 307.2 1159.816 312 2738 0
Arizona 86 2012 9.60E+07 1.20E+08 3550 4 0 1 0 58.7 0 1 0 41.3 18.37936 18.59896 37.08 1138.32 2433.72 315.804 433.68 660 2426 0
Arizona 86 2012 1.31E+08 1.49E+08 110 4 0 1 0 82 0 1 2 18 18.68941 18.82107 101.97 8494.56 3713.82 8 882.924 2048.304 934 4332 1
Arizona 86 2012 1.81E+08 1.99E+08 460 5 0 1 0 58.7 0 1 0 41.3 19.01667 19.10902 360.5 12812.22 9098.4 1110 3155.856 2109 10925 1
Arizona 86 2012 5.37E+07 3.92E+07 3550 2 0 1 0 58.7 0 1 2 41.3 17.79862 17.48499 210.12 10312.2 9235.08 1303.464 2696.6 2715 12235 0
Arizona 86 2012 2.28E+08 2.45E+08 3550 6 0 1 0 58.7 0 1 0 41.3 19.24457 19.31838 354.32 27260.52 9731.82 1711.284 7236.896 2559 18413 1
Arizona 86 2012 3.15E+08 3.79E+08 267 5 0 1 1 55.2 0 2 2 44.8 19.56899 19.7525 252.35 16108.86 15733.5 1894.188 3968.728 3487 12895 2
Arizona 86 2012 2.64E+08 2.81E+08 460 5 0 1 1 58.7 0 1 0 41.3 19.39099 19.45325 273.98 17960.16 16340.4 1704.816 4232.272 3447 16298 2
Arizona 86 2012 4.70E+08 5.17E+08 3550 8 0 1 1 58.7 0 1 0 41.3 19.96899 20.06368 273.98 17960.16 16340.4 1704.816 4232.272 3447 16298 1
Arizona 86 2012 3.94E+08 4.35E+08 3550 7 0 1 1 58.7 0 1 0 41.3 19.79191 19.89182 273.98 17960.16 16340.4 1704.816 4232.272 3447 16298 1
Arizona 86 2012 3.48E+07 3.67E+07 25 2 0 1 3 65.9 0 1 2 34.1 17.36395 17.41857 0
Arizona 86 2012 5.24E+07 5.62E+07 49 2 1 0 0 52.3 0 2 2 47.7 17.77366 17.8452 507.79 29487.18 40869.36 44.66 3096.06 7225.776 8762 29644 1
Arizona 86 2012 4.28E+08 4.54E+08 553 8 1 0 0 55.3 0 1 2 44.7 19.8756 19.9329 50.47 2233.8 2249.1 500.772 563.784 654 2095 0
Arizona 86 2012 1.22E+08 1.23E+08 89 3 1 0 3 43.9 1 1 2 56.1 18.61977 18.62993 91.67 4144.26 5121.42 788.256 1223.2 1544 3712 0
Arizona 86 2012 2.23E+08 2.16E+08 3550 4 1 1 0 58.7 0 1 0 41.3 19.22436 19.19189 244.11 29369.88 2147.1 89.71 5149.536 6878.832 264 12315 2
Arizona 86 2012 2.27E+08 2.68E+08 3550 6 1 1 0 58.7 0 1 0 41.3 19.24058 19.40528 397.58 38496.84 4977.6 1.88 2182.056 9723.328 1340 22069 1
Arizona 86 2012 9.23E+08 9.84E+08 244 5 1 1 0 58.7 0 1 0 41.3 20.64341 20.70665 327.54 32268.72 11889.12 1869.108 8493.456 2780 20464 2
Arizona 86 2012 2.72E+08 2.95E+08 3550 7 1 1 0 58.7 0 1 0 41.3 19.42014 19.50291 169.95 8433.36 12750 1059.324 2466.416 4690 13654 0
Arizona 86 2012 6.06E+08 6.80E+08 3550 8 1 1 1 58.7 0 1 0 41.3 20.22179 20.33736 585.04 37101.48 53716.26 129.3 4415.16 7460.408 10624 36275 0
Arizona 86 2012 1.98E+08 2.41E+08 3550 5 1 1 2 58.7 0 1 0 41.3 19.1031 19.30064 220.42 12159.42 24371.88 1554.48 3299.304 5620 18796 2
Arkansas 71 2012 8125045 7994666 49 2 0 0 0 84 0 1 2 16 15.91046 15.89429 111.24 8150.82 1690.14 717.768 2257.36 803 4634 2
Arkansas 71 2012 7.38E+07 7.72E+07 125 4 0 0 0 95.2 0 2 2 4.800003 18.11635 18.16157 120.51 11514.78 1907.4 704.808 2766.656 561 4925 1
Arkansas 71 2012 7.12E+07 7.71E+07 124 4 0 0 0 89 0 1 2 11 18.08072 18.16073 13.39 1.02 1 1 2
Arkansas 71 2012 2.28E+07 2.36E+07 33 2 0 0 0 68.2 1 0 2 31.8 16.9437 16.97513 25.75 1785 57.12 103.896 394.76 26 502 1
Arkansas 71 2012 1.05E+07 1.03E+07 85 3 0 0 0 71 1 0 2 29 16.16907 16.143 25.75 1164.84 44.88 178.392 306.912 22 395 1
Arkansas 71 2012 1.62E+07 1.88E+07 25 2 0 0 0 40.3 1 0 2 59.7 16.60155 16.75008 25.75 1051.62 194.82 117.936 259.096 62 414 2
Arkansas 71 2012 9525674 8233617 25 2 0 0 0 92.2 1 0 2 7.800003 16.0695 15.92374 25.75 2970.24 762.96 180.468 760.608 429 1243 2
Arkansas 71 2012 2.08E+07 2.22E+07 72 3 0 0 0 84.1 1 0 2 15.9 16.85083 16.91463 25.75 3277.26 839.46 177.708 684.992 144 1136 2
Arkansas 71 2012 1.90E+07 1.95E+07 35 2 0 0 0 58 1 0 2 42 16.75869 16.7843 25.75 1048.56 140.76 108.792 253.536 47 380 1
Arkansas 71 2012 7280002 6124331 26 2 0 0 0 95 1 0 2 5 15.80064 15.62778 25.75 2063.46 1147.5 203.184 529.312 427 1213 2
Arkansas 71 2012 8981868 8779914 25 2 0 0 0 46.8 1 0 2 53.2 16.01072 15.98798 25.75 2063.46 1147.5 203.184 529.312 427 1213 2
Arkansas 71 2012 1.80E+08 1.80E+08 333 6 0 0 2 41.4 0 2 2 58.6 19.00796 19.00953 226.6 21352.68 3790.32 16.25 1445.7 5354.28 1043 11444 1
Arkansas 71 2012 1.61E+08 1.64E+08 266 5 0 0 3 96 0 1 2 4 18.89993 18.91253 284.28 39680.04 10245.9 16.76 1947.264 8560.176 2906 17086 0
Arkansas 71 2012 5.86E+07 5.84E+07 125 4 0 0 3 95.4 0 1 2 4.599998 17.88697 17.88236 117.42 10665.12 2298.06 700.38 2274.04 863 4928 2
Arkansas 71 2012 1.34E+08 1.34E+08 146 4 0 0 3 82.4 0 1 2 17.6 18.71023 18.71331 172.01 20803.92 2783.58 1168.872 5972.552 939 9666 2
Arkansas 71 2012 2.37E+08 2.55E+08 375 6 0 0 3 79.6 0 2 2 20.4 19.28277 19.35728 172.01 20803.92 2783.58 1168.872 5972.552 939 9666 2
Arkansas 71 2012 3.19E+07 3.25E+07 80 3 0 0 3 83.5 1 0 2 16.5 17.2775 17.29597 59.74 3112.02 1345.38 344.82 821.768 550 2632 2
Arkansas 71 2012 2.39E+07 3.39E+07 143 4 0 0 3 94.1 1 0 2 5.900002 16.99044 17.34006 30.9 1881.9 263.16 171.948 603.816 73 815 1
Arkansas 71 2012 1.65E+07 1.69E+07 46 2 0 0 3 95.9 1 0 2 4.099998 16.62067 16.64345 25.75 2254.2 130.56 210.636 449.248 35 600 0
Arkansas 71 2012 1.85E+07 1.91E+07 41 2 0 0 4 76.7 0 1 2 23.3 16.73334 16.76492 2
Arkansas 71 2012 1.34E+07 1.19E+07 25 2 0 0 4 46.8 1 0 2 53.2 16.41199 16.29221 25.75 1712.58 548.76 140.916 385.864 227 834 1
Arkansas 71 2012 9563577 8258766 25 2 0 1 0 93.8 0 1 2 6.199997 16.07347 15.92679 220.42 29111.82 4643.04 1369.116 6231.648 1279 10879 0
Arkansas 71 2012 1.78E+08 1.75E+08 282 5 0 1 0 84 0 1 2 16 18.9969 18.9805 164.8 10821.18 2282.76 973.464 3209.232 913 8682 1
Arkansas 71 2012 1.58E+08 1.78E+08 141 4 0 1 0 76.6 0 1 2 23.4 18.88097 18.99704 25.75 1110.78 80.58 70.944 224.624 18 307 1
Arkansas 71 2012 1.02E+07 7574942 24 1 0 1 0 85.3 1 0 2 14.7 16.13752 15.84036 24.72 1094.46 60.18 53.4 264.656 17 377 1
Arkansas 71 2012 1.51E+08 1.56E+08 171 4 0 1 2 89.8 0 1 2 10.2 18.83054 18.86587 442.9 47683.98 10017.42 5 1928.376 9634.368 2162 20543 2
Arkansas 71 2012 3.57E+08 3.23E+08 409 7 0 1 2 55.3 0 1 1 44.7 19.69448 19.59453 142.14 21330.24 3384.36 1202.796 4393.512 1182 8000 1
Arkansas 71 2012 4.74E+08 4.73E+08 703 8 0 1 2 55.3 0 1 1 44.7 19.97661 19.97376 691.13 70966.5 12676.56 5.5 3352.536 13084.904 3029 32377 2
Arkansas 71 2012 2.22E+08 1.99E+08 374 6 0 1 3 72.8 0 1 2 27.2 19.21836 19.11002 302.82 26373.12 4982.7 1558.8 5163.016 1518 12147 0
Arkansas 71 2012 1.25E+07 1.36E+07 20 1 0 1 3 67.4 0 0 2 32.6 16.34282 16.42407 25.75 2405.16 158.1 142.2 444.8 49 668 2
Arkansas 71 2012 1.63E+07 1.99E+07 25 2 0 1 3 84 1 0 2 16 16.60686 16.80791 25.75 1399.44 181.56 169.704 384.752 62 727 2
Arkansas 71 2012 7635363 6872063 16 1 0 1 4 92.2 1 0 2 7.800003 15.8483 15.

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