Linear Regression代写、代做Python，c/c++编程语言、代写Java代写

日期：2019-05-04 10:45

IMPORTANT NOTE: Total points are 100. Submission via blackboard by Monday December 6 midnight local time!  Write concise answers, you can insert your answers after each question. Don’t include graphs!

Section 1 – Simple Linear Regression (35)

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The attached file in excel contains historical annual average temperatures taken at a DC station for a period of about 150 years.  Download the file into excel.  Each column represent the year and the average temperature for a given year.

Question 1:  (5) Compute the linear regression equation (coefficients) between the “year” variable and the “temperature” variable.  In other words, the dependent variable will be the temperature and the independent variable will be “year” variable.  Write down the equation, the correlation coefficient R and the standard error.

Question 2.  (10)

a. Has the annual temperature trend given by the regression line increased or decreased? Hint:  Which of the regression line coefficients expresses whether the linear relationship between temperature and time (in years) is increasing or decreasing?  

b. What is the rate of increase or decrease in temperature? Hint: the rate of increase or decrease in temperature is the amount of change in temperature for a change of 1 year.  Write down that amount.  

Question 3: (5) What is the predicted temperature (by the regression equation) and the residual for year = 1980 and year =1900?  

Question 4:  (10) Regression results include the analysis of variance.  What is the total sum of errors, the regression sum of errors and the residual sum of errors?  What is the ratio between the regression sum of errors and the total sum of errors and what does it represent?  

Question 5:  (5) Is the regression model significant at alpha = 0.05 and why?  Are the slope and intercept values significant at alpha = 0.05 and why?  

Section 2 –  Inference testing (30 points)

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A multi-media program designed to improve dietary behavior of low-income women was administered to a randomly selected group (treatment group).  A control group was also randomly chosen who was not subject to the multi-media program.  After two months, each individual from both groups was given a knowledge test, with scores varying from 0 to 6.   The idea behind this experiment was to evaluate the effectiveness of the multi-media program in improving dietary behavior among low-income women.

The summary statistics for the treatment and control groups are provided below:

Group n (sample size) x (mean score) s (sample standard deviation)

Treatment 165 5.08 1.15

Control 212  4.33 1.16

Question 1 (5 points) Which test would be the appropriate one here?

Question 2 (10 points) Determine the 95% confidence interval for the difference in population mean scores between the treatment and control. Assume equal population variances.  

Question 3 (15 points) Has the multi-media program been effective in improving behavior/increasing scores? Perform a one-sided hypothesis test with alpha = 0.05.

Write down the following:

1.State the null and the alternative hypothesis

2.write down the test statistic value and the P-value

3.Compare the P-value with alpha = 0.05

4.State your conclusion

Section 3 –   Inference Test with one and two sample proportions (35 points).

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Public Policy Polling Institute’s survey of 700 likely voters conducted in April 2009 found that Obama’s approval rating was 53%, down from 55% a month ago (in March 2009). Assume that the size of the sample (700) is the same for the April and March polls, and that 53 and 55% are the sample proportions in April and March, respectively.  Sample summary statistics are provided below:

Month           Sample size      Sample Proportion (in percent)

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March               700                  55

April                 700                  53

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Question 1 (10 points) What is the margin of error (in percent) for the April polling survey? Assume a 0.95 confidence level.

Question 2 (10 points) What is the margin of error (in percent) for the March polling survey? Assume a 0.95 confidence level.

Question 3 (15 points) Is the change in approval rating between March and April statistically significant? Conduct a two- sided significance test assuming a significance level alpha = 0.05. Our suspicion is that the true (national) approval rating in April is different than the true approval rating in March. Write down the following:

1)the null and alternative hypothesis

2)the value of the test statistic

3)The P-value

4)Draw the conclusion about whether the decrease in Obama’s approval rating from March to April is statistically significant at alpha = 0.05.