Question 2 – 15 marks This question is based on your work on MU123 up to and including Unit 6. (a) Describe in your own
Posted: Mon May 09, 2022 12:36 pm
Question 2 – 15 marks This question is based on your work on
MU123 up to and including Unit 6. (a) Describe in your own words
how you would expect the data points on a scatterplot to be
distributed (i.e. explain how they would look on a scatterplot) if
the following features were present. (i) A weak negative
relationship between the x and y variables [2] (ii) A positive
correlation between the x and y variables [2] (iii) A correlation
coefficient of r = −0.9 [2] (b) This question investigates the
relationship between the time taken to upload a file to the eTMA
system and the number of students using the eTMA system at a
particular time. A sample of 20 students were asked to record the
time at which their eTMA submission was received and the time taken
to upload their eTMA file. The researcher then checked to see how
many students were logged on to the eTMA system at the recorded
submission times. The results were displayed on a scatterplot with
the regression line included. The number of students logged on at
the submission time was displayed on the horizontal axis, and the
time taken to upload the file (in seconds) was displayed on the
vertical axis. The number of students logged on to the system at
the times recorded ranged from approximately 1500 to 4500. (i) The
regression line for the investigation is y = 0.0046x + 7.81. (1)
What does the variable x represent here? [1] (2) What does the
variable y represent here? [1] (ii) The correlation coefficient r
for the investigation is 0.97. What does this tell you about the
relationship between x and y? [2] (iii) Use the regression equation
from part (b)(i) to predict the time it takes to upload a file when
there are 2460 students logged on to the eTMA system. Give your
answer to the nearest whole second. [3] (iv) Can we conclude from
this investigation that increases in the number of students using
the eTMA system cause increases in upload times? Explain your
answer.
MU123 up to and including Unit 6. (a) Describe in your own words
how you would expect the data points on a scatterplot to be
distributed (i.e. explain how they would look on a scatterplot) if
the following features were present. (i) A weak negative
relationship between the x and y variables [2] (ii) A positive
correlation between the x and y variables [2] (iii) A correlation
coefficient of r = −0.9 [2] (b) This question investigates the
relationship between the time taken to upload a file to the eTMA
system and the number of students using the eTMA system at a
particular time. A sample of 20 students were asked to record the
time at which their eTMA submission was received and the time taken
to upload their eTMA file. The researcher then checked to see how
many students were logged on to the eTMA system at the recorded
submission times. The results were displayed on a scatterplot with
the regression line included. The number of students logged on at
the submission time was displayed on the horizontal axis, and the
time taken to upload the file (in seconds) was displayed on the
vertical axis. The number of students logged on to the system at
the times recorded ranged from approximately 1500 to 4500. (i) The
regression line for the investigation is y = 0.0046x + 7.81. (1)
What does the variable x represent here? [1] (2) What does the
variable y represent here? [1] (ii) The correlation coefficient r
for the investigation is 0.97. What does this tell you about the
relationship between x and y? [2] (iii) Use the regression equation
from part (b)(i) to predict the time it takes to upload a file when
there are 2460 students logged on to the eTMA system. Give your
answer to the nearest whole second. [3] (iv) Can we conclude from
this investigation that increases in the number of students using
the eTMA system cause increases in upload times? Explain your
answer.