STAT 1043 Homework 8

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New Brunswick Community College, Fredericton *

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1043

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Statistics

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Apr 3, 2024

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docx

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STAT 1043 Homework 8– Correlation and Regression Please submit through Dropbox by 10:00 pm on Thursday, March 28, 2024 Goal: Try some correlation analysis questions yourself Directions: Please label your solutions properly and write as clearly as you can. Please ensure that the solutions are written in order. Collaboration in solving problems on the assignments are acceptable; however, copying assignments is inappropriate and will be considered academic misconduct. For the calculation questions, it’s fine to use Excel or other software, but please take a picture/screenshot of your setup with the final answer or explain what you did on the software in writing to get your result. Activity: (The part to hand in for marks) 1. (9 marks) Dr. Phil, television’s most beloved and trusted doctor (no relation to the guy teaching your course), wants to investigate the relationship between stress and job satisfaction for his latest episode. To begin, he developed a profile for stress based on assigning points for significant events, such as the death of a spouse, a change in sleeping habits, a change in eating habits, and the birth of a child. Job satisfaction was also based on points assigned for salary, ability to get along with co- workers, and the job environment. Dr. Phil sampled 25 workers in the technology sector and found that the correlation between stress and job satisfaction was r = -0.536. a. (2 marks) Based on the value of r , does job satisfaction seem to increase or decrease as stress increases? Why? b. (7 marks) At the 0.05 significance level, is it reasonable to conclude there is a negative association between stress and job satisfaction? Use the 5-step process. 2. (11 marks) The city council of Hawkins, Illinois, is considering increasing the number of police in an effort to reduce crime (and the Stranger Things, which seems to be happening there). Before making a final decision, the council asks the chief of police to survey other cities of similar size to determine the relationship between the number of police and the number of crimes reported. The chief gathered the following sample information: City Police Number of Crimes Oxford 15 17 Starksville 17 13 Danville 25 5 Athens 27 7 Holgate 17 7 Carey 12 21 Whistler 11 19 Woodville 22 6

a. (1 mark) If we want to estimate crimes on the basis of the number of police officers, which is the independent variable, and which is the dependent variable? b. (2 marks) Use Excel to create a scatter diagram. Be sure to label the axis and provide a meaningful title. c. (3 marks) Compute the correlation coefficient r . d. (3 marks) Compute a and b for the regression equation and state the regression equation. e. (2 marks) Using the regression equation, estimate the number of crimes in a city that has 20 police officers.

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