First year retention in a college is affected by many variables including average SAT, high school GPA, % of students in

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First year retention in a college is affected by many variables
including average SAT, high school GPA, % of students in the top
10%of their graduating class, % of students in the top 20%of their
graduating class, and the average ACT score.Data was collected from
35 colleges in the southeast and a researcher in the Department of
Education is trying to build the best regression model to predict
first year retention.
a)Using Excel’s Correlation procedure, determine which of these
variables has the highest correlation with first year retention.
Which variable has the highest correlation with first year
retention?
b)Prepare a scatter plot showing the relationship between the
first-year retention and variable you identified in part a.Properly
format (trend line with equation, modify equation with variable
names rather than x & y, axes labels, etc.) this scatterplot
and paste into a Word document with a Figure number. Write an
interpretation which discusses the model fit and write the
regression equation.
c)Perform the backward stepwise procedure, which is the first
variable that is removed in the procedure?
d)Perform the backward stepwise procedure, which is the second
variable that is removed in the procedure?
e)Perform the backward stepwise procedure, which is the third
variable that is removed in the procedure?
f)After completing the backward stepwise procedure, which
independent variables remain in the model?
g)Create an ANOVA table for your best model (based on your
answer to part (f) (using Excel’s Regression procedure), format it
to show no more than 3 decimal places and remove duplicate columns.
Copy and paste it at of the end of the Word document you created in
part (b).
h)Based on your best model (part g), how should the researchers
estimate the first-year retention for a college with an
averageSATof 1100, a high school GPA of 3.4, 30 % of students in
the top 10%of their graduating class, 45% of students in the top
20%of their graduating class, and an average act score of 22.
i)Considering all five independent variables, does there appear
to be any multicollinearity among the independent variables?
j)Which of the following pairs of independent variables(if
any)indicate multicollinearity?

First Year Retention In A College Is Affected By Many Variables Including Average Sat High School Gpa Of Students In 1 (217.2 KiB) Viewed 87 times

1st year retention rate Avg SAT HS GPA % top 10% % top 20% Avg ACT 82.70% 1200.50 3.565 33.70% 60.50% 26.30 80.00% 1003.40 3.402 20.40% 37.00% 22.70 78.80% 1135.67 3.401 17.58% 41.76% 24.03 89.90% 1193.11 3.601 40.46% 65.32% 26.30 67.65% 1041.00 3.075 10.70% 19.70% 21.90 67.10% 1036.44 3.170 13.45% 30.57% 21.91 73.50% 1019.42 3.347 17.58% 41.76% 22.12 91.45% 1211.50 3.574 36.00% 68.40% 26.10 79.10% 1075.42 3.346 15.90% 33.47% 22.94 59.88% 932.00 2.718 2.50% 15.00% 19.50 88.50% 1194.60 3.617 36.30% 67.40% 26.00 67.00% 936.06 2.527 1.55% 5.17% 18.99 72.00% 1061.37 3.190 14.43% 29.49% 22.01 59.88% 901.00 2.623 2.90% 6.69% 19.00 63.20% 920.23 2.671 3.17% 10.32% 19.22 84.90% 1206.09 3.535 31.45% 56.40% 26.23 70.18% 993.00 2.997 1.80% 17.50% 20.70 65.70% 924.00 2.603 1.80% 6.00% 19.00 66.90% 924.80 2.738 5.20% 14.20% 19.00 76.40% 1010.68 3.329 14.63% 21.95% 21.90 87.70% 1148.90 3.477 32.60% 53.90% 24.10 68.80% 1037.90 3.179 13.70% 27.50% 21.80 67.70% 1013.24 2.905 5.44% 16.33% 21.06 86.60% 1162.25 3.494 31.53% 53.15% 25.54 67.00% 973.28 3.184 10.96% 23.29% 21.27 85.40% 1195.52 3.603 42.07% 63.79% 26.47 66.30% 1014.90 2.856 6.70% 16.30% 21.00 72.50% 980.87 3.339 7.79% 31.17% 21.61 73.10% 1013.30 2.839 5.90% 14.10% 21.10 76.43% 1133.20 3.281 18.20% 37.70% 23.80 75.40% 996.20 3.211 8.60% 20.70% 22.00 76.90% 1065.90 3.199 9.60% 22.90% 22.70 52.50% 970.00 3.188 23.33% 43.33% 20.97 72.55% 1025.40 3.278 21.10% 36.80% 21.60 76.70% 1077.93 3.237 11.65% 24.92% 22.94