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Homework 3
Department of Statistics, Florida State University
Homework 3
STA 2023
Fall 2023
Instructor: Sudipto Saha
DUE: November 9, 2023
There are 7 questions worth 43 points in total.
Read each question’s instructions carefully, show your work and include units wherever
asked. If you do not follow the instructions, you will be penalized.
This homework contains questions only from Simple Linear Regression. You may use respective
course materials to solve the questions. You will need a TI-84 plus or equivalent calculator.
You are encouraged to discuss with other students in your class to work on this homework. But
avoid plagiarism, it means, you can discuss a problem with your classmate, but your answer should
not be exactly same with your classmate. You should have your own words to write an answer. If
two or more submissions are identical, then the submitters will receive a score of zero.
Although you can discuss with your classmates, the submission should be individual and not
in groups.
To submit your solutions, you may write your work on a print-out of this homework or on separate
sheets of paper that properly reference each question. In both cases, be sure to include your name
on your papers. Make a PDF or MS word file of the solution and submit the same by uploading
the file to Canvas webpage under “Homework 3”.
This homework is due on Thursday, November 9, at 11:59 pm (EDT). Late submissions will
not be accepted without proper documentation.
1
Homework 3
Department of Statistics, Florida State University
1. The scatter plot of a data set is given below.
a) (2 point) What is the direction (positive or negative) of the correlation? No work required.
b) (2 point) If the circled point is removed, will the magnitude of correlation move closer to
zero or further away from zero? No work required.
2. (2 points) A group of students has been recording Amazon River’s low water level over time.
Identify the response variable and predictor variable in this case. No work required.
3. Below are some correlations provided for different data sets.
X and Y in data set A have correlation 0.123
X and Y in data set B have correlation -0.456
X and Y in data set C have correlation 0.789
X and Y in data set D have correlation -0.098
X and Y in data set E have correlation -0.123
X and Y in data set F have correlation 0.765
X and Y are the random variables and A through F are the datasets. Answer the following
questions. No work required.
a) (2 point) Which data set exhibits the strongest negative linear form?
b) (2 point) Which data set exhibits the weakest positive linear form?
c) (2 point) Which data set exhibits a straight line almost parallel to x-axis?
4. (4 points) Write the simple linear regression model as discussed in the class. State each and
every variable in words. Also include the assumptions.
2
Homework 3
Department of Statistics, Florida State University
5. (2 points) Which of the two models shown below appears to be a better fit for the data? Give
a brief reason in support of your answer.
6. (3 points) The scatterplot below shows the areas of some Galapagos Islands and the number
of endemic species that exist on each island.
A simple linear regression model is fitted. The value of R2 for the model is found out to be
47.85%. What is the value of the linear correlation for the data? Show all your work. Round
your answer to three decimal places.
3
Homework 3
Department of Statistics, Florida State University
7. The data below are the height-at-age-two of some children, and their eventual adult-height.
Perform a simple linear regression analysis on this data using your calculator.
a) (2 points) Identify the response variable and the predictor variable.
b) (2 points) Write down the estimated value of slope and intercept. Round your answer to
three decimal places. Include proper units.
c) (3 points) Write down the fitted regression equation properly.
d) (2 points) What is the value of coefficient of determination in percentage? Round your
answer to three decimal places after converting it to percentage.
4
Homework 3
Department of Statistics, Florida State University
e) (1 points) What is the amount (with direction) of linear association between adult-height
and height-at-age-two? Round your answer to three decimal places.
f) (4 points) Let, xm = the maximum value of predictor variable; and x0 = (xm – 2) inches.
Calculate the predicted value of response variable at x0 when the model is:
i) well-fitted.
ii) not well-fitted.
Show all your work. Round your answer to three decimal places. Include proper
units.
g) (2 points) If the predictor variable goes down by 1.53 inches, how might the response
variable be affected? Show all your work. Round your answer to three decimal places.
Include proper units and direction of change.
h) (6 points) Interpret the slope, the intercept and the R2 in words.
5
Homework 3
Department of Statistics, Florida State University
Homework 3
STA 2023
Fall 2023
Instructor: Sudipto Saha
DUE: November 9, 2023
There are 7 questions worth 43 points in total.
Read each question’s instructions carefully, show your work and include units wherever
asked. If you do not follow the instructions, you will be penalized.
This homework contains questions only from Simple Linear Regression. You may use respective
course materials to solve the questions. You will need a TI-84 plus or equivalent calculator.
You are encouraged to discuss with other students in your class to work on this homework. But
avoid plagiarism, it means, you can discuss a problem with your classmate, but your answer should
not be exactly same with your classmate. You should have your own words to write an answer. If
two or more submissions are identical, then the submitters will receive a score of zero.
Although you can discuss with your classmates, the submission should be individual and not
in groups.
To submit your solutions, you may write your work on a print-out of this homework or on separate
sheets of paper that properly reference each question. In both cases, be sure to include your name
on your papers. Make a PDF or MS word file of the solution and submit the same by uploading
the file to Canvas webpage under “Homework 3”.
This homework is due on Thursday, November 9, at 11:59 pm (EDT). Late submissions will
not be accepted without proper documentation.
1
Homework 3
Department of Statistics, Florida State University
1. The scatter plot of a data set is given below.
a) (2 point) What is the direction (positive or negative) of the correlation? No work required.
b) (2 point) If the circled point is removed, will the magnitude of correlation move closer to
zero or further away from zero? No work required.
2. (2 points) A group of students has been recording Amazon River’s low water level over time.
Identify the response variable and predictor variable in this case. No work required.
3. Below are some correlations provided for different data sets.
X and Y in data set A have correlation 0.123
X and Y in data set B have correlation -0.456
X and Y in data set C have correlation 0.789
X and Y in data set D have correlation -0.098
X and Y in data set E have correlation -0.123
X and Y in data set F have correlation 0.765
X and Y are the random variables and A through F are the datasets. Answer the following
questions. No work required.
a) (2 point) Which data set exhibits the strongest negative linear form?
b) (2 point) Which data set exhibits the weakest positive linear form?
c) (2 point) Which data set exhibits a straight line almost parallel to x-axis?
4. (4 points) Write the simple linear regression model as discussed in the class. State each and
every variable in words. Also include the assumptions.
2
Homework 3
Department of Statistics, Florida State University
5. (2 points) Which of the two models shown below appears to be a better fit for the data? Give
a brief reason in support of your answer.
6. (3 points) The scatterplot below shows the areas of some Galapagos Islands and the number
of endemic species that exist on each island.
A simple linear regression model is fitted. The value of R2 for the model is found out to be
47.85%. What is the value of the linear correlation for the data? Show all your work. Round
your answer to three decimal places.
3
Homework 3
Department of Statistics, Florida State University
7. The data below are the height-at-age-two of some children, and their eventual adult-height.
Perform a simple linear regression analysis on this data using your calculator.
a) (2 points) Identify the response variable and the predictor variable.
b) (2 points) Write down the estimated value of slope and intercept. Round your answer to
three decimal places. Include proper units.
c) (3 points) Write down the fitted regression equation properly.
d) (2 points) What is the value of coefficient of determination in percentage? Round your
answer to three decimal places after converting it to percentage.
4
Homework 3
Department of Statistics, Florida State University
e) (1 points) What is the amount (with direction) of linear association between adult-height
and height-at-age-two? Round your answer to three decimal places.
f) (4 points) Let, xm = the maximum value of predictor variable; and x0 = (xm – 2) inches.
Calculate the predicted value of response variable at x0 when the model is:
i) well-fitted.
ii) not well-fitted.
Show all your work. Round your answer to three decimal places. Include proper
units.
g) (2 points) If the predictor variable goes down by 1.53 inches, how might the response
variable be affected? Show all your work. Round your answer to three decimal places.
Include proper units and direction of change.
h) (6 points) Interpret the slope, the intercept and the R2 in words.
5
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