Simple Linear Regression Statistics and Standard Error Questions the questions and the needed information has been attach in the attached files. All the qu

Simple Linear Regression Statistics and Standard Error Questions the questions and the needed information has been attach in the attached files. All the questions has to come with equations. The questions are all about statistics and the excel file attachment is for the first problem sets in the Stat.doc Write concise answers, you can insert your answers after each question. Don’t
include graphs!
Section 1 – Simple Linear Regression (35)
——————————————————————————————-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)
——————————————————————————————-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
Treatment
Control
n (sample size)
165
212
x (mean score)
5.08
4.33
s (sample standard deviation)
1.15
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.
2.
3.
4.
State the null and the alternative hypothesis
write down the test statistic value and the P-value
Compare the P-value with alpha = 0.05
State your conclusion
Section 3 – Inference Test with one and two sample proportions (35
points).
———————————————————————————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)
————————————————————————–March
700
55
April
700
53
——————————————————————————
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.
Year
1871
1872
1873
1874
1875
1876
1877
1878
1879
1880
1881
1882
1883
1884
1885
1886
1887
1888
1889
1890
1891
1892
1893
1894
1895
1896
1897
1898
1899
1900
1901
1902
1903
1904
1905
1906
1907
1908
1909
1910
1911
1912
1913
1914
1915
1916
Temperature
54.8
54.8
54.8
56
52.2
54.3
55.5
56
55.8
55.6
56
54.9
54
55.1
53
53.4
54.8
53.6
55.1
56.3
55.4
54
53.7
56.4
54.2
55.5
54.9
56.1
54.4
56.5
54.1
54.8
54.3
52.2
54.1
55.9
53.5
55.4
55.2
55.2
56.4
54.5
57.3
54.9
55.6
55
1917
1918
1919
1920
1921
1922
1923
1924
1925
1926
1927
1928
1929
1930
1931
1932
1933
1934
1935
1936
1937
1938
1939
1940
1941
1942
1943
1944
1945
1946
1947
1948
1949
1950
1951
1952
1953
1954
1955
1956
1957
1958
1959
1960
1961
1962
1963
53
55.6
56.4
54.7
58
56.4
56.1
54.1
56.1
54.5
56.3
56
56.5
57.5
58.2
57.3
57.1
55.9
55.8
56.3
56.4
57.6
57.8
54.8
57.6
57.2
56.9
56.9
57.1
58
56.5
56.6
59
56.9
57.6
57.6
58.9
57.7
57.1
56.3
58
55.5
58.9
56.3
56.7
55.8
55.7
1964
1965
1966
1967
1968
1969
1970
1971
1972
1973
1974
1975
1976
1977
1978
1979
1980
1981
1982
1983
1984
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
2007
2008
2009
2010
57.5
56.8
56.8
56.4
57.5
57.2
57.7
57.9
56.7
59.3
58.8
59.4
57.9
58.6
58.1
58.1
59.5
59
57.7
58.4
57.8
58.2
57.8
58.1
57.1
56.9
60
60.2
56.7
57.7
58.3
57.9
56.9
58
60
58.9
57
58.5
59.3
56.4
58
58
59.1
59
59.2
57.4
59.8
2011
2012
2013
2014
2015
59.9
61.5
58.8
58.5
60.1

Purchase answer to see full
attachment