NEED BEFORE WEDNESDAY 8 pm EST I have no Idea how to do this I need help. This E
ID: 3133579 • Letter: N
Question
NEED BEFORE WEDNESDAY 8 pm EST
I have no Idea how to do this I need help.
This Excel file SAT Math shows the national average SAT Math scores for the years 1967-2005 (The College Board made significant changes to the SAT between the 2005 and 2006 exams; the class of 2005 was the last class to take the former version of the exam when it featured math and verbal sections).
In data sets that have large numbers such as "years", it is usually better to shift the data. Therefore, subtract 1966 from each Year value in the Excel file so that the shifted Year values range from 1 to 39.
Create a scatterplot with the shifted years as the explanatory variable x and the SAT Math scores as the response variable y.
Question 1. The scatterplot indicates that a linear model is not appropriate. The scatterplot also indicates that a ladder of powers transformation will not work for this data. A curvilinear (polynomial) regression model will work best. From the 2 polynomial models shown below, select the polynomial model that works best for this data. Base your decision on the results of the parameter hypothesis tests, the values of the standard errors and coefficients of determination, and analysis of the residuals. (one submission only)
y = 0 + 1x + 2x2 + y = 0 + 1x + 2x2 + 3x3 + (CORRECT)
Question 2. For the model selected in Question 1, consider the coefficient of the term with the highest power of x. What is the value of the test statistic for the hypothesis test that tests whether this coefficient is nonzero?
Question 3. What is the residual for 2004? Use 2 decimal places.
SAT Math Scores
Year
SATMath
1967
516
1968
516
1969
517
1970
512
1971
513
1972
509
1973
506
1974
505
1975
498
1976
497
1977
496
1978
494
1979
493
1980
492
1981
492
1982
493
1983
494
1984
497
1985
500
1986
500
1987
501
1988
501
1989
502
1990
501
1991
500
1992
501
1993
503
1994
504
1995
506
1996
508
1997
511
1998
512
1999
511
2000
514
2001
514
2002
516
2003
519
2004
518
2005
520
SAT Math Scores
Year
SATMath
1967
516
1968
516
1969
517
1970
512
1971
513
1972
509
1973
506
1974
505
1975
498
1976
497
1977
496
1978
494
1979
493
1980
492
1981
492
1982
493
1983
494
1984
497
1985
500
1986
500
1987
501
1988
501
1989
502
1990
501
1991
500
1992
501
1993
503
1994
504
1995
506
1996
508
1997
511
1998
512
1999
511
2000
514
2001
514
2002
516
2003
519
2004
518
2005
520
Explanation / Answer
Question 2. For the model selected in Question 1, consider the coefficient of the term with the highest power of x. What is the value of the test statistic for the hypothesis test that tests whether this coefficient is nonzero?
-5.536 or -5.54 ( two decimals)
Question 3. What is the residual for 2004? Use 2 decimal places.
-0.67
Regression Analysis
R²
0.922
Adjusted R²
0.915
n
39
R
0.960
k
3
Std. Error
2.497
Dep. Var.
SATMath
ANOVA table
Source
SS
df
MS
F
p-value
Regression
2,579.4570
3
859.8190
137.86
1.91E-19
Residual
218.2866
35
6.2368
Total
2,797.7436
38
Regression output
confidence interval
variables
coefficients
std. error
t (df=35)
p-value
95% lower
95% upper
Intercept
525.4852
1.7666
297.454
3.76E-61
521.8988
529.0716
x
-4.3279
0.3777
-11.460
2.14E-13
-5.0946
-3.5612
xx
0.1846
0.0218
8.469
5.42E-10
0.1403
0.2288
xxx
-0.0020
0.00035837
-5.536
3.16E-06
-0.0027
-0.0013
Regression Analysis
R²
0.922
Adjusted R²
0.915
n
39
R
0.960
k
3
Std. Error
2.497
Dep. Var.
SATMath
ANOVA table
Source
SS
df
MS
F
p-value
Regression
2,579.4570
3
859.8190
137.86
1.91E-19
Residual
218.2866
35
6.2368
Total
2,797.7436
38
Regression output
confidence interval
variables
coefficients
std. error
t (df=35)
p-value
95% lower
95% upper
Intercept
525.4852
1.7666
297.454
3.76E-61
521.8988
529.0716
x
-4.3279
0.3777
-11.460
2.14E-13
-5.0946
-3.5612
xx
0.1846
0.0218
8.469
5.42E-10
0.1403
0.2288
xxx
-0.0020
0.00035837
-5.536
3.16E-06
-0.0027
-0.0013
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