CSS 211: Statistical Methods ISpring 2021Homework No. 031. Question:Malaria is a leading cause of infectious disease and death worldwide. It is also a popularexample of a vector-borne disease that could be greatly affected by the influence of climatechange. Table 1 is a summary from a linear regression that uses dewpoint (°C) to predictmalaria prevalence in West Africa.Fig. 1: Regression(a) Write the equation of the least square regression line.(b) Find the correlation coefficient r.(c) Is there a strong correlation between dewpoint and malaria prevalence in West Africa?(d) Is there a negative association between dewpoint and malaria prevalence in WestAfrica?2. Question:John’s parents recorded his height at various ages between 36 and 66 months. Below is arecord of the results: Age(A, months)3648546066Height(H, inches)3438414345 (a) Determine the correlation coefficient between Age and Height.(b) Determine the equation of the least-squares regression line of John’s height on age.(c) John’s parents decide to use the least-squares regression line of John’s height on ageto predict his height at age 21 years (252 months). What conclusion can we draw?3. Question:Many high school students take either the SAT or the ACT. However, some students takeboth. Data were collected from 60 students who took both college entrance exams. Theaverage SAT score was 912 with a standard deviation of 180. The average ACT score was21 with a standard deviation of 5. The correlation between the two variables equals 0.817.(a) To predict the SAT score (y) from a student’s ACT score (x), what is the equation ofthe least-squares regression line?(b) What fraction of the variation in the values of the SAT scores is accounted for by thelinear relationship between SAT and ACT scores?4. Question:A researcher at a large company has collected data on the beginning salary and currentsalary of 48 randomly selected employees. The least-squares regression equation for predicting their current salary from their beginning salary is yˆ = -2532.7 + 2.12x.(a) The current salaries had a mean of $32,070 with a standard deviation of $15,300. Thebeginning salaries had a mean of $16,340 with a standard deviation of $5,970. What isthe correlation between current and beginning salary?(b) Mr. Joseph Keller started working for the company earning $22,000. What do youpredict his current salary to be?(c) Mrs. Kathy Jones started working for the company earning $19,000. She currentlyearns $40,000. What is the residual for Mrs. Jones?5. Question:A student organization is trying to decide whether or not to offer more movies on campus.They want to determine whether this idea will appeal to members of both genders. Arandom sample of 1000 students was asked if they were in favor of more movies oncampus. The results by gender are shown in the table below in Figure 2.Fig. 2: Summary(a) What proportion of the sampled students is in favor of more movies on campus?(b) What proportion of the sampled females is in favor of more movies on campus?(c) What proportion of the sampled males is in favor of more movies on campus?(d) To answer the original question regarding whether or not to offer more movies oncampus, which distribution should the student organization study?i. The joint distribution of gender and opinion.ii. The marginal distribution of gender.iii. The conditional distribution of gender given opinion.iv. The conditional distribution of opinion given gender.
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