Getting Started Linear regression is one of the most common yet powerful statistical tools because it allows you to make predictions of a dependent variable based u
Getting Started
Linear regression is one of the most common yet powerful statistical tools because it allows you to make predictions of a dependent variable based upon an independent variable i.
Upon successful completion of this assignment, you will be able to:
- Develop regression models and predict future values.
Background Information
There have been many pronouncements that have been made regarding the COVID-19 pandemic. This assignment will show you how you can examine the data for yourself, and make your own decisions concerning how well the country is coping with the pandemic.
Instructions
- Review the rubric to make sure you understand the criteria for earning your grade.
- Read chapters IV, and XIV, in the online textbook. Watch the videos and powerpoints that go with each chapter.
- Go to The COVID Tracking Project website and download the data for all states.
- Sort the data by states and find the date for your state of residence.
- Create a new column AR in the database labeled % positive. The formula to calculate % positive should be = AD1/AP1. Format the cell for percentage. Copy the cell down the column for all dates of your state.
- Create a new column AS in the database labeled % tested. From the World Population Review website, determine the population of your state. The formula to calculate % tested should be = AH1/the population of your state. Format the cell for percentage. Copy the cell down the column for all dates of your state.
- Using the data, develop a linear regression time series analysis for deaths (column D), % tested, and % positive. Answer the following questions:
- What is the null and alternative hypothesis for each variable?
- What was the r squared for each variable? What does this mean?
- What was the p-value of each test? What does this mean?
- For those tests which were significant, use the model to predict the value of the variable seven days after the end of the workshop.
- Write a short report (1 to 2 pages for each variable) that includes the results of your analysis. Present the results and discuss the implications of your findings. Include whatever graphs or statistical output you may have generated in answering these questions along with a short explanation of your analysis. What conclusions concerning COVID19 may you draw from your analysis?
- When you have completed your assignment, submit a copy to your instructor using the Assignment submission page.
- The assignment is due by the end of the workshop.
6/11/22, 8:16 AM Preview Rubric: 5.2 Assignment: Linear Regression and Time Studies (75 points) – 3SU2022 Data Analytics & Research (BADM-707-01B) – In…
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5.2 Assignment: Linear Regression and Time Studies (75 points) Course: 3SU2022 Data Analytics & Research (BADM-707-01B)
Criteria Excellent Competent Needs Improvement
Inadequate/Faili ng
Criterion Score
Statistical
tools
/ 20
Discussion of
the output of
the regression
model
/ 20
20 points
Statistical tools
were
constructed
correctly and
strongly
supported the
discussion.
18 points
(16-18 points)
Statistical tools
were
constructed
correctly and
generally
supported the
discussion.
15 points
(12-15 points)
Statistical tools
were
constructed
correctly and
but did not
support the
discussion.
11 points
(0-11 points)
Statistical tools
were not
constructed
correctly but
did not
support the
discussion.
20 points
Demonstrated
clear, insightful
critical thinking
in the
Discussion of
the output of
the regression
model.
19 points
(16-19 points)
Demonstrated
competent
critical thinking
in the
Discussion of
the output of
the regression
model.
15 points
(12-15 points)
Demonstrated
limited critical
thinking in
Discussion of
the output of
the regression
model.
11 points
(0-11 points)
Demonstrated
little to no
critical thinking
in the
Discussion of
the output of
the regression
model.
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Criteria Excellent Competent Needs Improvement
Inadequate/Faili ng
Criterion Score
Discussion of
conclusions
concerning
COVID-19
/ 2020 points
Demonstrated
clear, insightful
critical thinking
in the
Discussion of
the
conclusions
concerning
COVID 19.
19 points
(16-19 points)
Demonstrated
competent
critical thinking
in the
Discussion of
the
conclusions
concerning
COVID 19.
15 points
(12-15 points)
Demonstrated
limited critical
thinking in
Discussion of
the
conclusions
concerning
COVID 19.
11 points
(0-11 points)
Demonstrated
little to no
critical thinking
in the
Discussion of
the
conclusions
concerning
COVID 19.
6/11/22, 8:16 AM Preview Rubric: 5.2 Assignment: Linear Regression and Time Studies (75 points) – 3SU2022 Data Analytics & Research (BADM-707-01B) – In…
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Total / 75
Criteria Excellent Competent Needs Improvement
Inadequate/Faili ng
Criterion Score
Grammar,
Spelling,
Length, and
Citation
/ 1515 points
Sentence
structure is
complete with
correct
spelling,
punctuation,
capitalization,
varied diction,
and word
choices.
Assignment
length is
correct with
sources
correctly cited.
14 points
(12-14 points)
Sentence
structure has
minor errors
(fragments,
run-ons) with
correct
spelling,
punctuation,
capitalization,
and limited
diction and
word choices.
Assignment
length is
correct with
sources
correctly cited.
11 points
(9-11 points)
Sentence
structure has
several errors
in sentence
fluency with
multiple
fragments/run-
ons; poor
spelling,
punctuation,
and/or word
choice.
Assignment
length is
inappropriate
with several
format and
citation errors.
8.25 points
(0-8 points)
Sentence
structure has
serious and
persistent
errors in
sentence
fluency,
sentence
structure,
spelling,
punctuation,
and/or word
choice.
Assignment
length is
inappropriate
with several
format and
citation errors
or sources not
cited.
6/11/22, 8:16 AM Preview Rubric: 5.2 Assignment: Linear Regression and Time Studies (75 points) – 3SU2022 Data Analytics & Research (BADM-707-01B) – In…
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Overall Score
Excellent 69 points minimum
Competent 62 points minimum
Needs Improvement 54 points minimum
Inadequate/Failing 0 points minimum
,
1
Linear Regression and Time Studies 2
Linear Regression and Time Studies
Linear Regression and Time Studies
In this assignment, we are going to perform linear regression on the COVID tracking data for the state of my residence, i.e., Maryland, for the following variables:
1. “%tested”
2. “%positive” and
3. “deaths”.
In linear regression for the data, we will first be choosing an independent variable x and a dependent variable y and try to find a best possible linear relationship between the two. We will be trying to find coefficients a and b such that y = bx+c. Here b is the slope of the line and c is the y intercept.
1. LINEAR REGRESSION FOR THE VARIABLE “% TESTED”
For the variable % tested we choose the independent variable, x to be the “date” and the dependent variable y to be “% tested”. We formulate the null and alternate hypotheses as follows:
Null Hypothesis: “ The slope which means that y is independent of x. ”
Alternate Hypothesis: “ The slope ≠ 0 which means that y is dependent on x.”
Output:
First, we note that the equation of the straight line we obtained is y = 0.0038x – 165.24. Hence the value of slope b = 0.0038 and c =- 165.24.
In the following two tables, we summarise the output data we got by performing the linear regression:
|
Regression Statistics |
||||||||
|
Multiple R |
0.9624 |
|||||||
|
R Square |
0.926214 |
|||||||
|
Adjusted R Square |
0.926014 |
|||||||
|
Standard Error |
0.114243 |
|||||||
|
Observations |
372 |
|||||||
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
|
Intercept |
-165.242 |
2.431183 |
-67.9679 |
4.1E-211 |
-170.023 |
-160.462 |
-170.023 |
-160.462 |
|
% tested |
0.003759 |
5.52E-05 |
68.15053 |
1.6E-211 |
0.003651 |
0.003868 |
0.003651 |
0.003868 |
We observe the following from the output data:
1. r-squared value: The r-squared value, 0.926214 is very close to 1. This means that there is a strong positive linear relationship between the two variables x and y.
2. p-value: We find that the p-value is 1.6E-211which is way less than 0.05. Hence we reject the null hypothesis and we conclude that the alternate hypothesis is significant in the 0.05 significance level.
Graph of the data and the linear fit:
Using the p-value, we concluded that this model is significant. Now, we use this model predicted outcomes for the next 7 days after the end of the workshop and put it in the following table:
|
DATE |
% tested |
|
08-03-2021 |
1.144655 |
|
09-03-2021 |
1.148415 |
|
10-03-2021 |
1.152174 |
|
11-03-2021 |
1.155933 |
|
12-03-2021 |
1.159692 |
|
13-03-2021 |
1.163451 |
|
14-03-2021 |
1.16721 |
2. LINEAR REGRESSION FOR THE VARIABLE “% POSITIVE”
For the variable % positive, we choose the independent variable, x to be the “date” and the dependent variable y to be “% positive”. We formulate the null and alternate hypotheses as follows:
Null Hypothesis: “ The slope which means that y is independent of x. ”
Alternate Hypothesis: “ The slope ≠ 0 which means that y is dependent on x.”
Output:
First, we note that the equation of the straight line we obtained is y = -0.0004x + 19.331. Hence the value of slope b = -0.0004 and c = 19.331.
In the following two tables, we summarise the output data we got by performing the linear regression:
|
Regression Statistics |
|
|
Multiple R |
0.802194 |
|
R Square |
0.643515 |
|
Adjusted R Square |
0.642488 |
|
Standard Error |
0.032809 |
|
Observations |
349 |
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
|
Intercept |
19.3307 |
0.768533 |
25.15271 |
3.32E-80 |
17.81913 |
20.84227 |
17.81913 |
20.84227 |
|
% positive |
-0.00044 |
1.74E-05 |
-25.0278 |
1.01E-79 |
-0.00047 |
-0.0004 |
-0.00047 |
-0.0004 |
We observe the following from the output data:
1. r-squared value: The r-squared value, 0.643515 is in the middle of 0 and 1. This means the linear relationship between the two variables x and y is not very weak and at the same time not very strong as well.
2. p-value: We find that the p-value is 1.01E-79 is way less than 0.05. Hence we reject the null hypothesis and we conclude that the alternate hypothesis is significant in the 0.05 significance level.
Graph of the data and the linear fit:
Using the p-value, we concluded that this model is significant. Now, we use this model predicted outcomes for the next 7 days after the end of the workshop and put it in the following table:
|
DATE |
% positive |
|
08-03-2021 |
0.019669 |
|
09-03-2021 |
0.019233 |
|
10-03-2021 |
0.018797 |
|
11-03-2021 |
0.018361 |
|
12-03-2021 |
0.017924 |
|
13-03-2021 |
0.017488 |
|
14-03-2021 |
0.017052 |
3. LINEAR REGRESSION FOR THE VARIABLE “DEATHS”
For the variable deaths, we choose the independent variable, x to be the “date” and the dependent variable y to be “deaths”. We formulate the null and alternate hypotheses as follows:
Null Hypothesis: “ The slope which means that y is independent of x. ”
Alternate Hypothesis: “ The slope ≠ 0 which means that y is dependent on x.”
Output:
First, we note that the equation of the straight line we obtained is y = 19.335x – 848470. Hence the value of slope b = 19.335 and c = -848470.
In the following two tables, we summarise the output data we got by performing the linear regression:
|
Regression Statistics |
|
|
Multiple R |
0.965519 |
|
R Square |
0.932227 |
|
Adjusted R Square |
0.932036 |
|
Standard Error |
538.7689 |
|
Observations |
357 |
|
|
Coefficients |
Standard Error |
t Stat |
P-value |
Lower 95% |
Upper 95% |
Lower 95.0% |
Upper 95.0% |
|
Intercept |
-848470 |
12197.61 |
-69.5603 |
6.5E-209 |
-872458 |
-824481 |
-872458 |
-824481 |
|
deaths |
19.33474 |
0.276689 |
69.87885 |
1.4E-209 |
18.79058 |
19.87889 |
18.79058 |
19.87889 |
We observe the following from the output data:
1. r-squared value: The r-squared value, 0.932227 is very close to 1. This means that there is a strong positive linear relationship between the two variables x and y.
2. p-value: We find that the p-value is 1.4E-209 and it is way less than 0.05. Hence we reject the null hypothesis and we conclude that the alternate hypothesis is significant in the 0.05 significance level.
Graph of the data and the linear fit:
Using the p-value, we concluded that this model is significant. Now, we use this model predicted outcomes for the next 7 days after the end of the workshop and put it in the following table:
|
DATE |
deaths |
|
08-03-2021 |
7343.826 |
|
09-03-2021 |
7363.16 |
|
10-03-2021 |
7382.495 |
|
11-03-2021 |
7401.83 |
|
12-03-2021 |
7421.165 |
|
13-03-2021 |
7440.499 |
|
14-03-2021 |
7459.834 |
% tested 44262 44261 44260 44259 44258 44257 44256 44255 44254 44253 44252 44251 44250 44249 44248 44247 44246 44245 44244 44243 44242 44241 44240 44239 44238 44237 44236 44235 44234 44233 44232 44231 44230 44229 44228 44227 44226 44225 44224 44223 44222 44221 44220 44219 44218 44217 44216 44215 44214 44213 44212 44211 44210 44209 44208 44207 44206 44205 44204 44203 44202 44201 44200 44199 44198 44197 44196 44195 44194 44193 44192 44191 44190 44189 44188 44187 44186 44185 44184 44183 44182 44181 44180 44179 44178 44177 44176 44175 44174 44173 44172 44171 44170 44169 44168 44167 44166 44165 44164 44163 44162 44161 44160 44159 44158 44157 44156 44155 44154 44153 44152 44151 44150 44149 44148 44147 44146 44145 44144 44143 44142 44141 44140 44139 44138 44137 44136 44135 44134 44133 44132 44131 44130 44129 44128 44127 44126 44125 44124 44123 44122 44121 44120 44119 44118 44117 44116 44115 44114 44113 44112 44111 44110 44109 44108 44107 44106 44105 44104 44103 44102 44101 44100 44099 44098 44097 44096 44095 44094 44093 44092 44091 44090 44089 44088 44087 44086 44085 44084 44083 44082 44081 44080 44079 44078 44077 44076 44075 44074 44073 44072 44071 44070 44069 44068 44067 44066 44065 44064 44063 44062 44061 44060 44059 44058 44057 44056 44055 44054 44053 44052 44051 44050 44049 44048 44047 44046 44045 44044 44043 44042 44041 44040 44039 44038 44037 44036 44035 44034 44033 44032 44031 44030 44029 44028 44027 44026 44025 44024 44023 44022 44021 44020 44019 44018 44017 44016 44015 44014 44013 44012 44011 44010 44009 44008 44007 44006 44005 44004 44003 44002 44001 44000 43999 43998 43997 43996 43995 43994 43993 43992 43991 43990 43989 43988 43987 43986 43985 43984 43983 43982 43981 43980 43979 43978 43977 43976 43975 43974 43973 43972 43971 43970 43969 43968 43967 43966 43965 43964 43963 43962 43961 43960 43959 43958 43957 43956 43955 43954 43953 43952 43951 43950 43949 43948 43947 43946 43945 43944 43943 43942 43941 43940 43939 43938 43937 43936 43935 43934 43933 43932 43931 43930 43929 43928 43927 43926 43925 43924 43923 43922 43921 43920 43919 43918 43917 43916 43915 43914 43913 43912 43911 43910 43909 43908 43907 43906 43905 43904 43903 43902 43901 43900 43899 43898 43897 43896 43895 43894 43893 43892 43891 1.3350384044939225 1.3295766371947539 1.3229185832642534 1.3160389459224366 1.3104790818005498 1.3053193537941872 1.3034992043440901 1.3003233403171677 1.2939292410306531 1.2866502919163603 1.2787166495533049 1.2725861751735572 1.2677639332110668 1.2656973051896021 1.2620392004795697 1.2567363665200655 1.2525430983032382 1.2455844888974181 1.2396574623819294 1.2358399297264038 1.2341966842944183 1.2309387156999101 1.2249312333029316 1.2181505171268809 1.2107963879266057 1.2043350222473701 1.1993286220479451 1.1969611088139418 1.193194850296005 1.1851807520514601 1.1779232358564167 1.1709558884142872 1.1651051960650478 1.162696960284471 1.1604379305955912 1.1562489489626138 1.1486270731403316 1.1406118208155194 1.1319095609944612 1.1242471274942147 1.1184953563107418 1.1142209727379861 1.10 84944264517835 1.1010346164727483 1.0931718676118254 1.0846005134667978 1.078414148628392 1.0733203680658736 1.0684781770016203 1.0642347887274715 1.0565313029434322 1.0473237208339186 1.0383718499379104 1.031146483121741 1.0254858842793824 1.0203330807546234 1.0131579988643851 1.0032367005438685 0.99407231401007279 0.98466655983180762 0.97812918972354168 0.97181785447905145 0.96771559373472904 0.96186424191105135 0.95750181850076399 0.94989609980222367 0.94107496971363647 0.9352468643639138 0.92860612163742229 0.92519169273239388 0.91877368749748578 0.91436707929982275 0.90808772856559694 0.90115005747319732 0.8935876992189844 0.88702427987040011 0.87784142805232801 0.87119392571284238 0.86416854452013014 0.85816650278726869 0.85088293735190679 0.84601172941236213 0.83993500219934725 0.83446383738943086 0.82786744431892445 0.81939435186522458 0.80854072155736212 0.80059454917997652 0.79249785176201681 0.78656043852412261 0.77989974669586815 0.77248791348222945 0.76451684594479274 0.7556304278867999 0.7464122941862712 0.7412510823624221 0.73538736539302363 0.73032655855242723 0.72581740207958667 0.71934647402099372 0.71477829458591269 0.70697671197915535 0.70008998528712529 0.69258599052071446 0.68777809212726015 0.68267590326565142 0.67444978398914768 0.66595740190812336 0.65915624202448098 0.65190812334018522 0.64666513668596948 0.64209168145538098 0.6363488131768269 0.63163785752582335 0.62543434635201822 0.62015541834090737 0.61494590001444249 0.6104520763222957 0.60640471682497354 0.60250557420769091 0.59751566086922692 0.59149861609289089 0.58566787284541455 0.58106078441846554 0.57689455465361439 0.57361581261429517 0.56919502571620573 0.56428952510586217 0.55885149888647745 0.55416972497937489 0.54959973198958822 0.54590354263073582 0.54208073417970282 0.53848544440993196 0.53323190616470106 0.52787202766627161 0.52251841417500733 0.51750195699039603 0.5146866606126913 0.51172463117243339 0.50765715770473874 0.50278891740016707 0.49676676169693323 0.49220863924703845 0.48748746174223911 0.48387832300926098 0.48079313671762425 0.47684370917441055 0.47203251340876401 0.46648303600928276 0.46201179931665259 0.45722681765993411 0.45380843190827502 0.45088267356213141 0.44765619487205865 0.44330959884829385 0.43868239645097235 0.43358762667679618 0.42963325307529415 0.42679372101197671 0.42430700777322522 0.4213555299239824 0.416401722811023 0.41118544487156405 0.40638908728078244 0.40248137149580016 0.39932281867288683 0.3969406321326282 0.39408032662449988 0.38931793196729797 0.38319619562385954 0.37913317360862436 0.3746251712160511 0.37023983106902786 0.36710551393172725 0.36394053123303916 0.3600633161408347 0.35457269683498432 0.35084435809725795 0.34778588052037807 0.3461518677305308 0.34401632463024917 0.34032821383326772 0.33757111607475537 0.33292314023262304 0.32807056244596433 0.32395544195009229 0.32190612513263678 0.31965484426840873 0.31646776917603286 0.31232874273176736 0.30812739595306915 0.30359317945156788 0.30005262606018762 0.29801204727904146 0.29589018827335745 0.2922553300372801 0.28876984276150963 0.28406152500825 993 0.27921669604625288 0.27624230146027423 0.27396233345797399 0.27131470845624289 0.26564306341704041 0.26142720820069654 0.25588762291779188 0.2519076946818003 0.24698768563381099 0.24401757763168222 0.24119090531991436 0.23632200554090424 0.22961646945083586 0.22618604829067523 0.22147360882218525 0.21872046791030356 0.21513259722796516 0.21243254400837797 0.20839590097068042 0.20447450109110046 0.19936291471874404 0.19464239668838315 0.19040708697610526 0.18781090098057254 0.18386328699206456 0.18000618587023257 0.17637231684581289 0.1706226889542648 0.16662957122950436 0.1639844192569174 0.16051871621430017 0.15713066628680938 0.15469802995201004 0.14993349200288322 0.14695711899358924 0.14297207983069973 0.14018728414577286 0.13663683863781598 0.13409538902067386 0.13227078811811716 0.12878546571095631 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6.8878807722973258E-3 5.5794834864303245E-3 5.3480079585375229E-3 4.9139089094337157E-3 4.3531907681492316E-3 3.9197511934838652E-3 3.4192100947071243E-3 3.0011033007355118E-3 2.5155652454333043E-3 2.1769251212938362E-3 1.9156083750615784E-3 1.699960233691362E-3 1.1929892591398211E-3 8.9292838964915298E-4 3.4210236494128368E-4 1.5744952217779562E-4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
Date
% tested
% positive 44262 44261 44260 44259 44258 44257 44256 44255 44254 44253 44252 44251 44250 44249 44248 44247 44246 44245 44244 44243 44242 44241 44240 44239 44238 44237 44236 44235 44234 44233 44232 44231 44230 44229 44228 44227 44226 44225 44224 44223 44222 44221 44220 44219 44218 44217 44216 44215 44214 44213 44212 44211 44210 44209 44208 44207 44206 44205 44204 44203 44202 44201 44200 44199 44198 44197 44196 44195 44194 44193 44192 44191 44190 44189 44188 44187 44186 44185 44184 44183 44182 44181 44180 44179 44178 44177 44176 44175 44174 44173 44172 44171 44170 44169 44168 44167 44166 44165 44164 44163 44162 44161 44160 44159 44158 44157 44156 44155 44154 44153 44152 44151 44150 44149 44148 44147 44146 44145 44144 44143 44142 44141 44140 44139 44138 44137 44136 44135 44134 44133 44132 44131 44130 44129 44128 44127 44126 44125 44124 44123 44122 44121 44120 44119 44118 44117 44116 44115 44114 44113 44112 44111 44110 44109 44108 44107 44106 44105 44104 44103 44102 44101 44100 44099 44098 44097 44096 44095 44094 44093 44092 44091 44090 44089 44088 44087 44086 44085 44084 44083 44082 44081 44080 44079 44078 44077 44076 44075 44074 44073 44072 44071 44070 44069 44068 44067 44066 44065 44064 44063 44062 44061 44060 44059 44058 44057 44056 44055 44054 44053 44052 44051 44050 44049 44048 44047 44046 44045 44044 44043 44042 44041 44040 44039 44038 44037 44036 44035 44034 44033 44032 44031 44030 44029 44028 44027 44026 44025 44024 44023 44022 44021 44020 44019 44018 44017 44016 44015 44014 44013 44012 44011 44010 44009 44008 44007 44006 44005 44004 44003 44002 44001 44000 43999 43998 43997 43996 43995 43994 43993 43992 43991 43990 43989 43988 43987 43986 43985 43984 43983 43982 43981 43980 43979 43978 43977 43976 43975 43974 43973 43972 43971 43970 43969 43968 43967 43966 43965 43964 43963 43962 43961 43960 43959 43958 43957 43956 43955 43954 43953 43952 43951 43950 43949 43948 43947 43946 43945 43944 43943 43942 43941 43940 43939 43938 43937 43936 43935 43934 43933 43932 43931 43930 43929 43928 43927 43926 43925 43924 43923 43922 43921 43920 43919 43918 43917 43916 43915 43914 5.8377369069068701E-2 5.8498880644486884E-2 5.8651598351860484E-2 5.8815887551911403E-2 5.8945022832245113E-2 5.9054623332029446E-2 5.9063345884941498E-2 5.9112760852376836E-2 5.92712128635128E-2 5.9473648129603755E-2 5.9712680831575764E-2 5.9850831542249495E-2 5.9941679223766413E-2 5.9931957849192773E-2 5.9767456260880404E-2 6.0019646700479913E-2 6.0220580686093074E-2 6.0386792186856594E-2 6.0510864186135958E-2 6.0565177694283337E-2 6.0557383500618026E-2 6.0595110217005213E-2 6.0739121223859459E-2 6.0874339896494795E-2 6.1051676414295847E-2 6.1179219137180302E-2 6.1239123062345184E-2 6.118669862402551E-2 6.1212087966598348E-2 6.1099195702996871E-2 6.1475645023988688E-2 6.155068499785564E-2 6.1588926697544073E-2 6.1557678498706234E-2 6.1519100066178292E-2 6.1218675648645388E-2 6.1624900745293046E-2 6.1697455505016548E-2 6.1844214390013877E-2 6.186067881313069E-2 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