R Questions
STA 106 SS2 2020
R Quesitons – Due Monday, August 24th by 5pm.
Details
* This is an individual asignment and should be completed on your own.
* You may use R Markdown, Word, LaTex, Google Docs, etc. to submit your work.
* All answers with necessary output should be in the body of the work, and all code should be placed in an appendix.
* You may use resources on Canvas to complete the work.
* Submit your document to Canvas.
Problem I
I. Online you will find the file GSK.csv. The csv file has the following columns:
Column 1. sysbp: The systolic blood pressure of the subject (mmHg).
Column 2. gender: The gender, with levels F and M.
Column 3. married: Y if the subject was married, N if not.
Column 4. exercise: With levels L = low, M = medium, H = high.
Column 5. age: The age of the subject in years.
Column 6. stress: With levels LS = low, MS = medium, HS = high.
Column 7. educatn: With levels LE = low, ME = medium, HE = high.
Source: Data are part of a larger case study for the 2003 Annual Meeting of the Statistical Society of Canada.
(a) Find the average and standardard deviation of systolic blood pressure by stress level. Which group had the highest
average? Does it appear that the standard deviations are approximately equal?
(b) Find the average and standard deviation of age by exercise level. Which group has the lowest average age? Which
group seems to differ the most from its group mean?
(c) Create a boxplot of systolic blood pressure by education level. Does there appear to be a trend? Explain your
answer.
(d) Create a histogram of systolic blood pressure by marriage category. Does one group tend to vary more than the
other? Explain your answer.
II. For each of the following, use a plot or a function to justify your answers
(a) Which exercise group had the most subjects?
(b) Which stress group had the most highly educated subjects?
(c) Which stress group had the highest average age?
(d) Which gender group had the lowest average systolic blood pressure?
III. Using R, and assuming equal variance by group, test if the average systolic blood pressure for married vs. non-married
subjects is equal.
(a) Find the test-statistic.
(b) Find the exact p-value.
(c) Find and interpret the 95% confidence interval for the true difference.
(d) What is your conclusion about how systolic blood pressure may differ by marriage category? Explain and be specific.
1
Problem 2
I. Use the data Cancer.csv. The csv file has the following columns:
Column 1. Survival: The survival time of the patient in days
Column 2. Organ: The organ where cancer was present – Stomach, Bronchus, Colon, Ovary, Breast
Data Source : From the article Supplemental Ascorbate in the Supportive Treatment of Cancer: Reevaluation of
Prolongation of Survival Times in Terminal Human Cancer by Ewan Cameron and Linus Pauling, Proceedings
of the National Academy of Sciences of the United States of America, Vol. 75, No. 9 (Sep., 1978), pp. 4538-4542.
(a) Create a group box plot of Survival by Organ type. Does there appear to be significant differences in the
groups? Explain your answer.
(b) Find the sample averages of Survival by Organ type. Do you believe you would reject the null hypothesis of
Single Factor ANOVA based on these values? Explain.
(c) Do you believe the standard deviations of each population are equal? Explain.
(d) What level of would you suggest if concluding that the true average survival time was equal when in reality
it was not, would be considered the most severe error?
II. Continue with the Cancer dataset.
(a) Find the value of SSTO, SSA, SSE.
(b) Find the value of MSTO, MSA, MSE.
(c) Find the value of the test-statistic, and the corresponding p-value.
(d) State your conclusion in terms of the problem if = 0.05.
III. Diagnostic Tests
(a) Plot the QQplot, and residuals vs. fitted values. Does there appear to be a violation of the assumptions of
ANOVA? Explain your answer.
(b) Find and interpret the p-value of the Shaprio-Wilks test.
(c) Find and interpret the p-value of the Brown-Forsythe test.
(d) Based on your analyses above, would you want to transform the data? Explain.
2 sbp gender married exercise age stress educatn
133 F N H 60 MS ME
115 M N L 55 MS ME
140 M N L 18 HS HE
132 M Y M 19 HS ME
133 M N M 58 MS HE
138 F N H 55 MS HE
133 F Y L 22 HS LE
67 F Y H 52 MS ME
138 M Y L 46 MS LE
130 M Y H 38 MS LE
103 F N M 28 HS ME
137 M N M 54 MS LE
140 M N L 38 MS HE
131 F Y L 23 MS HE
134 M N H 23 LS HE
107 F Y H 18 LS ME
131 F Y M 24 HS HE
120 M Y H 40 MS LE
113 M Y L 18 HS LE
127 M Y H 56 MS HE
117 F N H 20 MS ME
139 F N M 56 HS HE
132 M N H 57 HS ME
124 F N H 45 LS LE
116 M N H 24 LS HE
115 M Y H 43 LS LE
131 F N L 61 MS ME
130 F N M 22 MS LE
124 F Y M 28 LS LE
139 M Y L 25 MS ME
130 M N M 61 LS HE
103 F Y L 44 MS LE
114 F N L 55 HS LE
135 M N M 53 HS LE
126 M N M 43 LS LE
133 M N L 43 HS HE
125 M Y H 50 MS LE
138 M N L 23 MS LE
138 M N M 33 HS LE
132 M N L 64 HS HE
114 M N M 29 LS ME
130 F N H 31 LS LE
127 F Y L 24 LS HE
131 F Y H 26 LS HE
101 M Y L 54 LS ME
130 F N L 42 MS HE
130 M Y M 24 HS HE
115 F Y M 40 HS ME
135 F N M 54 HS ME
134 F Y L 19 HS LE
131 M Y H 29 LS ME
112 F N H 36 MS LE
86 F N M 58 MS LE
132 M N L 25 MS HE
134 M N L 49 LS ME
122 M N L 43 HS LE
122 M N L 61 MS HE
137 M Y H 60 MS ME
137 M N L 32 MS HE
105 F N H 43 HS LE
136 M N H 53 LS HE
119 F N H 35 MS ME
139 F N H 41 MS ME
131 F N M 26 MS ME
125 M Y L 30 LS ME
121 M N H 54 HS HE
114 M N H 34 HS LE
100 M Y M 46 LS LE
135 M Y H 45 MS ME
129 F Y M 26 LS ME
120 M Y H 22 MS LE
137 M Y L 47 LS HE
132 M Y H 59 MS HE
113 F N H 23 HS ME
135 F Y M 38 HS LE
128 F Y H 56 LS ME
135 F Y L 42 MS LE
127 M Y H 33 LS ME
133 M Y L 45 HS LE
131 F Y L 57 HS LE
135 F Y L 25 MS ME
132 F Y H 32 LS HE
137 F N L 53 HS HE
138 M N L 22 MS HE
116 F Y H 40 LS HE
139 F N H 61 HS LE
137 M Y H 39 LS ME
128 M Y H 37 HS HE
134 F N H 36 HS HE
138 M N L 19 HS ME
134 F Y L 59 LS ME
111 F Y M 48 MS ME
139 M N L 45 HS HE
100 F N H 33 LS ME
135 F N H 40 MS HE
139 F N L 56 LS HE
125 M N H 38 MS HE
111 F Y H 42 HS HE
113 F Y H 56 LS HE
131 M Y L 62 MS HE
104 M N L 60 HS LE
134 M N L 26 LS LE
109 M Y L 51 LS ME
102 M Y L 27 MS HE
130 F N L 18 MS LE
139 F N H 41 LS ME
77 F Y H 20 LS LE
100 F N M 21 MS ME
135 M Y L 59 MS LE
139 M N M 62 HS LE
127 M N H 55 MS ME
110 F Y H 18 LS HE
132 F N M 38 HS ME
136 F N M 39 LS ME
135 M Y L 27 MS HE
139 M Y H 53 HS LE
123 M Y M 46 MS LE
138 F Y H 58 MS ME
123 M Y M 24 MS HE
134 M N H 52 LS ME
121 F Y M 41 MS LE
139 M Y M 60 LS HE
133 F N M 46 HS HE
137 F N L 26 LS HE
77 M Y H 40 LS HE
105 F Y L 57 LS HE
106 F N H 36 LS ME
102 M Y L 51 LS ME
139 M Y H 36 LS ME
130 F Y L 64 LS HE
135 F Y L 38 LS HE
135 F N L 21 MS LE
125 M N H 23 LS LE
134 F N L 45 HS ME
109 F Y H 26 HS HE
132 F Y H 44 MS ME
134 M N L 62 LS HE
125 M Y L 45 LS ME
124 M N M 32 HS HE
125 M N L 58 LS LE
138 F N M 53 HS LE
138 F Y L 30 MS ME
113 M N H 56 MS LE
111 F Y H 56 MS ME
112 M N H 22 LS HE
130 F N H 48 HS LE
114 F Y L 56 LS LE
108 F N L 36 MS LE
101 F N M 39 MS ME
134 F N L 25 MS ME
135 F Y H 63 MS LE
109 F Y M 19 MS ME
128 M N H 58 MS LE
137 F N H 40 HS ME
130 F N L 30 HS ME
135 F N L 37 LS LE
102 F N L 38 HS LE
137 M N H 44 LS LE
128 M N M 18 MS LE
112 F N M 32 LS ME
140 F N L 45 MS HE
138 F N H 53 LS ME
132 M N L 42 MS LE
130 M Y M 32 HS LE
88 F N M 38 LS ME
95 F N L 55 LS HE
130 F Y M 50 MS ME
138 F N H 46 LS LE
138 F N L 63 LS HE
133 F N H 35 LS ME
122 F N M 46 HS HE
120 F N M 23 MS HE
135 F Y M 61 HS LE
114 F Y H 45 LS LE
133 M Y M 40 HS ME
132 M Y M 35 MS HE
137 F N L 20 LS LE
120 F N H 27 LS HE
137 F Y L 23 MS HE
130 F Y H 61 MS LE
93 F Y H 30 HS ME
139 M N H 57 MS ME
122 M N M 25 HS HE
115 F N H 27 HS HE
135 M N H 47 LS ME
112 M N L 24 HS LE
72 M Y H 32 HS HE
104 M N M 57 LS HE
126 M N L 36 HS LE
100 F Y M 23 LS HE
139 M N M 48 LS HE
112 F Y L 18 LS HE
139 M Y H 40 LS HE
128 F N M 39 LS LE
130 M N L 50 HS ME
109 F Y H 33 LS LE
132 F N H 33 LS HE
136 M N H 23 MS LE
138 M Y M 38 LS LE
113 M N H 28 MS ME
131 M N H 38 MS LE
133 F N M 61 HS LE
80 M N H 52 MS ME
131 M Y H 63 HS LE
112 F Y M 32 MS HE
120 F N M 33 MS LE
107 M Y M 50 LS LE
133 M N M 26 LS ME
138 F N H 62 HS ME
134 M N L 20 HS LE
121 M Y L 24 LS HE
121 M N M 50 HS LE
118 M N H 46 HS LE
84 F N H 39 HS LE
117 F Y H 31 MS LE
84 M N H 43 HS LE
135 M N M 32 HS ME
132 M Y H 20 HS LE
132 M N H 37 MS ME
111 M N L 60 HS HE
114 M N L 62 LS HE
134 M Y L 27 LS HE
132 M Y L 46 MS ME
138 M N M 51 MS ME
109 F Y L 22 HS ME
114 F N L 39 HS HE
104 F N M 26 HS ME
130 F Y L 63 LS ME
136 M N L 49 LS ME
130 M Y L 46 MS ME
111 M N M 58 MS ME
102 F N H 35 HS HE
120 M Y H 52 LS LE
137 F N L 18 HS LE
131 M N L 39 MS LE
113 F N L 18 LS HE
131 F N L 37 MS LE
137 M N M 62 HS HE
119 M N M 30 MS HE
137 M N H 61 MS ME
138 F N M 21 LS ME
105 M N M 40 HS ME
73 M Y M 55 MS LE
126 F Y M 30 HS HE
107 F N M 29 LS LE
124 F N H 30 HS LE
80 M N H 36 MS ME
135 M N H 36 HS LE
136 F Y H 30 LS ME
134 M N H 45 HS HE
154 M N M 48 MS LE
151 M Y M 50 MS ME
174 F Y M 64 MS HE
146 F Y M 57 LS ME
148 F Y L 18 HS HE
172 F Y M 48 HS HE
153 M N L 25 HS ME
172 M N M 30 HS HE
171 F N M 33 HS HE
146 M Y H 28 LS ME
174 F Y L 54 MS ME
180 M N L 27 HS HE
165 F N L 59 HS HE
154 F Y M 44 HS LE
142 F Y L 39 LS ME
177 M Y M 56 MS HE
152 M Y M 28 MS HE
213 F Y H 36 HS HE
191 M Y M 55 MS ME
150 F Y L 26 HS HE
159 M Y L 43 HS ME
144 M N L 19 LS LE
146 M N H 25 HS LE
145 F N M 48 MS HE
196 F N L 51 LS LE
172 M Y H 35 HS HE
178 F N H 35 MS ME
150 F N M 33 HS ME
222 F Y L 42 HS ME
161 M Y L 61 LS HE
144 F Y L 58 MS ME
148 F N M 41 LS HE
166 M Y H 18 LS LE
154 F N L 58 HS ME
141 F N H 41 HS ME
148 F N L 61 MS ME
205 M Y L 50 HS ME
144 M Y H 50 HS LE
143 M N H 27 LS LE
203 M N L 48 MS LE
156 F N L 35 HS LE
176 M Y L 33 MS ME
174 F Y H 59 HS ME
161 M Y L 22 HS ME
152 M Y L 25 LS LE
169 M N M 19 LS ME
209 M N H 36 HS ME
201 F N H 60 LS LE
148 M Y M 21 HS LE
194 F Y H 20 MS HE
155 M N L 51 LS LE
176 F Y L 23 LS ME
145 F Y M 25 HS ME
142 F Y L 30 MS HE
182 M N H 57 MS LE
168 F N L 23 LS LE
165 M N H 28 MS LE
141 F Y L 26 MS HE
197 M Y L 54 LS LE
191 M N M 45 LS ME
196 F Y L 56 HS ME
149 F Y L 18 LS ME
180 F Y M 56 HS ME
174 F N H 21 HS HE
160 M Y H 43 LS ME
169 M N L 43 LS LE
147 F Y H 55 MS LE
149 M Y M 29 LS ME
178 F N H 28 MS HE
155 M Y M 60 HS LE
143 F N H 52 MS HE
203 F N H 49 LS LE
187 F Y H 28 MS ME
168 M Y M 26 LS LE
179 F N H 59 HS HE
169 M Y H 33 LS HE
153 M Y M 22 HS HE
173 M N M 45 HS LE
188 F Y L 53 HS ME
153 M Y M 21 LS LE
163 F Y H 48 MS ME
142 F Y L 52 MS LE
170 F Y L 21 LS LE
179 F N L 46 HS HE
160 F Y L 43 MS LE
176 M N L 40 MS HE
143 M N H 32 MS HE
162 F N M 46 LS LE
221 M N L 58 HS LE
142 F Y L 26 MS HE
169 F Y H 55 HS ME
212 F N L 53 MS HE
201 M Y L 50 LS ME
175 F Y H 25 HS LE
149 M N M 32 MS HE
141 F Y L 30 MS HE
149 F Y M 49 MS HE
154 M N M 43 HS HE
147 M N L 48 LS LE
141 F N H 55 HS HE
175 M N H 36 MS LE
164 M N L 32 MS LE
168 F N L 34 MS HE
148 F N H 32 HS HE
224 M N L 23 LS ME
210 F N L 25 MS LE
148 M N L 47 MS LE
198 F N M 27 HS LE
144 M Y M 21 HS ME
159 F Y L 35 HS HE
206 M N H 54 MS HE
154 M Y L 50 HS LE
144 F N L 43 LS ME
149 M N L 39 HS ME
142 F N M 31 HS ME
207 F Y H 33 MS ME
192 M Y L 38 MS ME
182 M Y M 61 LS ME
183 M N H 31 MS HE
148 M N M 31 MS HE
147 M Y L 43 MS HE
146 M Y L 34 HS HE
151 F Y H 47 HS ME
144 F Y H 24 MS LE
211 M N L 28 MS LE
141 F N H 38 HS HE
147 F Y M 59 HS LE
164 M Y H 51 HS ME
193 F Y L 51 MS HE
169 M N H 53 MS ME
172 M Y L 19 LS LE
187 M N L 63 HS ME
142 F Y L 55 HS ME
194 F N L 37 LS HE
149 M N M 40 HS LE
143 F Y M 45 LS LE
184 F Y L 36 LS LE
198 M N L 53 HS ME
143 F Y L 33 MS LE
161 F Y M 38 MS ME
188 F N M 62 LS HE
148 F N L 38 MS HE
167 M Y H 42 HS LE
181 F Y L 53 HS HE
144 F N L 53 MS LE
150 M Y M 49 MS ME
157 F N M 36 MS HE
165 M Y M 34 MS LE
175 F Y L 57 LS HE
162 F N L 44 LS HE
199 F Y L 59 MS HE
192 F N H 27 MS LE
216 F Y M 18 HS HE
199 M Y M 52 HS LE
174 F Y H 21 MS HE
141 M N M 22 LS ME
146 F Y H 36 MS HE
192 M Y L 30 HS LE
164 F Y H 28 LS ME
162 M N L 29 MS LE
178 M N L 63 HS HE
168 M N M 28 HS ME
141 F N M 28 LS LE
186 F Y M 36 LS HE
145 M Y H 44 HS LE
142 F N M 56 MS LE
175 F N L 45 LS HE
145 F N H 51 MS HE
147 F Y H 50 MS HE
179 M N H 55 MS LE
191 M N H 38 HS ME
184 F Y H 43 MS HE
144 F Y L 39 MS HE
178 M N L 23 HS ME
182 M N L 36 HS ME
168 M Y L 18 MS HE
214 F Y L 20 LS LE
148 F N H 50 MS HE
181 M Y M 29 MS LE
142 F Y L 64 HS HE
163 M Y H 50 LS LE
173 F N H 54 MS HE
181 F N H 43 MS LE
184 M N L 35 HS LE
147 M Y M 34 HS ME
176 F N M 19 MS HE
151 M Y H 29 HS ME
142 F Y L 20 LS HE
147 M Y L 40 LS ME
185 F N M 54 MS ME
203 F Y M 59 MS LE
142 F Y H 59 HS HE
168 M Y M 35 LS LE
147 F N H 34 HS HE
148 F Y H 41 HS ME
198 F Y L 58 HS LE
158 F N L 42 MS LE
165 F N M 27 LS HE
145 F N M 62 MS ME
148 F Y H 53 HS ME
172 F Y L 36 HS ME
162 F N M 42 LS LE
182 M N L 19 HS LE
148 F Y L 23 MS HE
148 F N H 39 HS ME
150 F N L 55 HS LE
143 F Y L 19 MS ME
209 M Y H 39 MS LE
151 F Y H 55 LS HE
152 M N L 42 MS LE
163 M N L 45 HS HE
212 F Y L 32 LS HE
159 M N L 27 HS LE
188 F Y L 51 LS LE
169 F N H 18 LS HE
145 M Y M 20 HS ME
188 F Y H 47 LS HE
142 F N L 41 LS HE
197 M N M 44 HS ME
142 M Y M 53 HS ME
175 F Y L 61 MS LE
141 M N L 59 HS ME
148 F Y M 43 MS LE
215 M Y H 52 HS LE
151 F Y L 41 MS HE
159 M N M 45 HS LE
160 F Y L 42 HS HE
167 M Y L 56 LS ME
142 M Y L 60 HS HE
144 F Y H 59 LS LE
143 M Y L 39 HS HE
173 M N M 23 MS ME
148 F Y M 46 HS HE
142 M N L 26 HS HE
144 F N H 62 LS ME
188 M Y L 30 LS HE
147 F N H 55 MS LE
158 M Y L 19 MS ME
179 F N M 32 HS LE
167 M Y L 28 LS ME
148 F N H 48 LS LE
162 F Y M 34 MS HE
165 F Y L 31 HS LE
181 F Y L 40 HS ME
142 F Y L 54 MS HE
146 F N H 49 HS HE
181 F N M 22 MS ME
145 M Y H 42 LS HE
180 M Y H 60 LS LE
174 F N L 24 LS LE Survival Organ
124 Stomach
42 Stomach
25 Stomach
45 Stomach
412 Stomach
51 Stomach
1112 Stomach
46 Stomach
103 Stomach
876 Stomach
146 Stomach
340 Stomach
396 Stomach
81 Bronchus
461 Bronchus
20 Bronchus
450 Bronchus
246 Bronchus
166 Bronchus
63 Bronchus
64 Bronchus
155 Bronchus
859 Bronchus
151 Bronchus
166 Bronchus
37 Bronchus
223 Bronchus
138 Bronchus
72 Bronchus
245 Bronchus
248 Colon
377 Colon
189 Colon
1843 Colon
180 Colon
537 Colon
519 Colon
455 Colon
406 Colon
365 Colon
942 Colon
776 Colon
372 Colon
163 Colon
101 Colon
20 Colon
283 Colon
1234 Ovary
89 Ovary
201 Ovary
356 Ovary
2970 Ovary
456 Ovary
1235 Breast
24 Breast
1581 Breast
1166 Breast
40 Breast
727 Breast
3808 Breast
791 Breast
1804 Breast
3460 Breast
719 Breast
