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Statistics homework for r studio. Questions submitted below in photos

AT&T
<
Math 552 (7521), Spring 2018
PDF HW_VII.pdf
abline (a=beta0,b=beta1)
drive.google.com
1:13 PM
HW_VII.pdf - Google Drive
3. Draw the regression line on the scatter plot in the part (1) by using the following
command:
where beta0 and betal are the calculated estimates from part (2). Do you think the
fit of the linear regression line is reasonable?
4. What are the interpretations of Bo and B₁?
Now for further inferences, let us use the "lm" command in R-Studio.
5. Let us test whether the B₁ is meaningful in this model under 0.01 significance level.
(a) State the hypotheses.
(b) What is the test statistic and p-value from the "lm" result.
(c) Conclude and interpret your result.
6. Obtain the 90% confidence interval for ₁ by using "confint" command. Interpret the
interval result.
7. Suppose we can reasonably expect the RPPG of Guinea Pigs is 0.98. Then, what is the
predicted winning percentage of Guinea Pigs? In addition, what is the 90% prediction
interval of winning percentage of guinea pigs? (Use "predict" command) Interpret this
prediction interval.
New Order
Now, instead of using RPPG, let us use a model as follows:
Bo + ₁ x PPG + ₂ × OPPG+ €
8. What is the coefficient of determination, R²2, of this model? What is the meaning of
the value?
=
Page
Winning Percentage
This is an example of multiple linear regression model and the result can be
obtained by the following commands:
fit<-lm (Win_P~PPG+OPPG) ; summary (fit)
9. Are those regression coefficients ₁ and 3₂ meaningful in this model?
10. What is the coefficient determination, R², of this model? Is this very different from
the R² in part (8)? Based on this observation, do you think RPPG was a effective
combination of PPG and OPPG?
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AT&T
<
Math 552 (7521), Spring 2018
PDF HW_VII.pdf
1:13 PM
drive.google.com
3. Find out the correlations between x; and y; for i = 1, 2, 3, 4.
(Round off to three decimal places.)
HW_VII.pdf - Google Drive
4. Find out the linear regression lines based on xi and Yi for i=1, 2, 3, 4.
(Round off to two decimal places.)
5. Lastly, visualize four scatter plots of Xi and yi
linear regression lines.
Variable
Team
W
L
Win P
6. What is the implication of the result from this Anscombe's data?
Briefly write down your finding.
Description
Team Name
# of Win
# of Loss
Problem #1. The following is the variable descriptions of NBA 2017-2018 regular season
data.
Winning Percentage
= # of Win / # of Game
for i
Variable
GB
PPG
OPPG
SRS
Playoff
Bo = Y – BLX; Bị
In our class, we predicted the winning percentage (Win_P) of our new team, Columbia
Guinea Pigs, by defining a new explanatory variable EPPG (PPG-EPPG). In this question,
let us define a similar measure, RPPG=PPG/OPPG which also reflects the both defensive
and offensive strengths of each team and use this for the prediction. The data can be obtained
by the following commands:
1, 2, 3, 4 super-imposed by their
download.file("http://people.stat.sc.edu/taeho/teaching/lab/NBA.RData",
destfile = "NBA.RData"); load ("NBA. RData"); attach (NBA)
=
=
1. Plot a scatter plot between the Winning Percentage and RPPG. From the visual ob-
servation, do you think a “linear” regression based on RPPG is an appropriate model
to predict winning percentage?
2. Suppose we decide to use the following model:
Winning Percentage
=
New Order
Description
Games Behind
Points per Game
Opponent Points per Game
Simple Rating System
Playoff Team
The intercept and slope parameters can be estimated by the least square estimators as
follows:
Bo + ₁ x RPPG + €
Σ₁ (Xi - X)(Yi – Y)
Σ₁₁(X₂ – X)²
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where Y Winning Percentage and X RPPG under our setting. Please find out the
values of least square estimators Bo and ₁ without using the command "Im". That
is, we can only use basic commands "mean", "sum", and etc. in R-Studio to calculate
the two estimates.
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AT&T
<
Math 552 (7521), Spring 2018
PDF HW_VII.pdf
1:13 PM
drive.google.com
HW_VII.pdf - Google Drive
Homework VII
STAT 509: Statistics for Engineers
April 22, 2018
Include all R code and output for the questions. Do not just "write in" the R
code you used. Also, do not just write the answer and say this is what R gave
you. I want to see your code and your answers accompanying your code.
Problem #1. The following is Anscombe's data which contains four sets of explanatory
and response variables.
Set
II Set III
Set
IV
Y4
6.58
5.76
7.71
X2 Y2 X3 Y3 X4
10 9.14 10 7.46 8
8 8.14 8 6.77 8
8.74 13 12.74 8
8.77 9
11
8.1 14
6.13 6
3.1 4
7.11
8
8.84
7.81
8
8.47
8.84
8
7.04
6.08
8 5.25
5.39
19
12.5
9.13 12
8.15
8
5.56
7.26 7
6.42
8
7.91
4.74 5
5.73 8
6.89
Set
I
X1 Y1
10 8.04
6.95
7.58 13
8
13
9
8.81 9
11
8.33
14
11 9.26
9.96 14
7.24 6
4.26 4
6
10.84 12
4
12
7
5 5.68 5
4.82 7
The data can be obtained by the following commands:
Please answer the following questions by using any commands of R-Studio.
1. Find out the sample means of x; and y, respectively for i = 1, 2, 3, 4.
(Round off to two decimal places.)
download.file("http://people.stat.sc.edu/taeho/teaching/lab/Anscombe. RData",
destfile = "Anscombe. RData"); load("Anscombe. RData"); attach (Anscombe)
2. Find out the sample variances of x; and y; respectively for i = 1, 2, 3, 4.
(Round off to three decimal places.)
New Order
1
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