Question

Build a simple linear regression for (1) all 50 states, (2) Eastern Time zone states, (3) Central Time zone states, (4) Mountain Time zone states, and (5) Pacific, Alaska, and Hawaii Time zone states. Compare your results in all five parts and state your judgements. You may use charts and tables in the comparison. Your answers should have values for the coefficient of determination, AOV table, significance levels, residual plots, and the regression fit with their interpretations.

Data source: Kaiser Family Foundation, 4/20/2020, 5:38PM. (ET = eastern time, CT = central time, MT = mountain time, PT = Pacific time). Some states have a mix of two different time zones which I ignored here).

States	Time zone	X = Number of COVID-19 Cases	Y = Deaths from COVID-19
Alabama	CT	5,041	169
Alaska	PT	321	9
Arizona	MT	5,068	191
Arkansas	CT	1,923	41
California	PT	33,404	1205
Colorado	MT	9,730	420
Connecticut	ET	19,830	1331
Delaware	ET	2,745	72
District of Columbia	ET	2,927	105
Florida	ET	26,660	789
Georgia	ET	18,947	733
Hawaii	PT	580	10
Idaho	MT	1,672	45
Illinois	CT	31,513	1349
Indiana	ET	11,686	569
Iowa	CT	3,159	79
Kansas	CT	2,043	101
Kentucky	ET	2,960	148
Louisiana	CT	24,523	1328
Maine	ET	875	35
Maryland	ET	13,684	465
Massachusetts	ET	38,077	1706
Michigan	ET	32,000	2468
Minnesota	CT	2,470	143
Mississippi	CT	4,512	169
Missouri	CT	5,889	200
Montana	MT	433	10
Nebraska	CT	1,511	28
Nevada	PT	3,830	159
New Hampshire	ET	1,390	41
New Jersey	ET	88,722	4496
New Mexico	MT	1,845	55
New York	ET	252,595	18611
North Carolina	ET	6,842	202
North Dakota	CT	627	9
Ohio	ET	12,919	509
Oklahoma	CT	2,680	143
Oregon	PT	1,957	75
Pennsylvania	ET	33,914	1348
Rhode Island	ET	5,090	155
South Carolina	ET	4,446	123
South Dakota	CT	1,685	7
Tennessee	ET	7,238	152
Texas	CT	19,751	507
Utah	MT	3,213	27
Vermont	ET	816	38
Virginia	ET	8,984	300
Washington	PT	12,111	643
West Virginia	WV	902	24
Wisconsin	CT	4,499	230
Wyoming	MT	313	2

Answer 1

Solution:

Excel Output

1.

In the above table, our regression model is,

Y ( Death from COVID-19) = Intercept ( B0) + (B1) * Number of COVID-19

Y ( Death from COVID-19) = -162.097 + 0.071 * number of COVID-19

2.

In the above result the P-value(0.000) < 0.05, then we reject the null hypothesis that means they stiatisticaly insignificant.

3.

Here the value of the coefficient of determination( R-square) is 0.92.

R-squared is a statistical measure of how close the data are to the fitted regression line. It is also known as the coefficient of determination, or the coefficient of multiple determination for multiple regression.

R-squared is always between 0 and 100%:

• 0% indicates that the model explains none of the variability of the response data around its mean.
• 100% indicates that the model explains all the variability of the response data around its mean.

here the value of R-square is near to 100% that means the line fit data well.

4.

Residual plot:

In this plot (on the right) each point is one day, where the prediction made by the model is on the x-axis, and the accuracy of the prediction is on the y-axis. The distance from the line at 0 is how bad the prediction was for that value.

Since

Residual = Observed – Predicted

positive values for the residual (on the y-axis) mean the prediction was too low, and negative values mean the prediction was too high; 0 means the guess was exactly correct.

In a simple model like this, with only two variables, you can get a sense of how accurate the model is just by relating Number of COVID-19 cases to death cases of COVID-19. Here’s the regression run where the model is very accurate.

5.

Line Fit Plot:

The value of R-squared is 0.92 which indicates the line of the data is fit well.

In the line fit plot the maximum number of points are near to line that means our line is fit well for these data.

Let me know in the comment section if anything is not clear. I will reply ASAP!
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