Consider the following data set and the Minitab output. Derive (i.e., calculate)
ID: 3063326 • Letter: C
Question
Consider the following data set and the Minitab output. Derive (i.e., calculate) each number that has a superscript next to it in the upper right-hand corner (and bolded)..
Show all of your work in complete detail.
Data Display
Row X Y
1 3 14
2 5 16
3 7 20
4 5 13
5 8 19
6 9 23
7 10 24
8 14 22
9 20 38
10 22 39
Descriptive Statistics: X, Y
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
X 10 0 10.30 2.03 6.43 3.00 5.00 8.50 15.50 22.00
Y 10 0 22.801 2.863 9.052 13.00 15.50 21.00 27.50 39.00
Regression Analysis: Y versus X
The regression equation is
Y = 8.860 + 1.353 X
Coefficients
Term Coef SE Coef T-Value P-Value
Constant 8.868 1.649 5.3910 0.00111
X 1.3534 0.1375 9.876 0.0007
S = 2.6464112 R-Sq = 92.4%13 R-Sq(adj) = 91.5%14
Analysis of Variance
Source DF SS MS F P
Regression 115 681.57218 681.57221 97.3223 0.00024
Error 816 56.02819 7.00322
Total 917 737.60020
Prediction for Y
Regression Equation
Y = 8.86 + 1.353 X
Variable Setting
X 14
Fit SE Fit 95% CI 95% PI
27.807625 0.97878326 (25.550527, 30.064728) (21.300929, 34.314230)
Correlation: X, Y
Pearson correlation of X and Y = 0.96131
Explanation / Answer
I will give you interpretation of each step .
Regression Analysis: Y versus X
The regression equation is
Y = 8.860 + 1.353 X
Coefficients
Term Coef SE Coef T-Value P-Value
Constant 8.868 1.649 5.3910 0.00111
X 1.3534 0.1375 9.876 0.0007
S = 2.6464112 R-Sq = 92.4%13 R-Sq(adj) = 91.5%14
Analysis of Variance
Source DF SS MS F P
Regression 115 681.57218 681.57221 97.3223 0.00024
Error 816 56.02819 7.00322
Total 917 737.60020
Prediction for Y
Regression Equation
Y = 8.86 + 1.353 X
Interpritation - you can see the above R-square value is 92.4% That means response variable (Y) explane 92.4 % Variation in regressor variable (X) .
and The P-vaue is less than 0.05 so the model is significant .
That means the model is very good.
Correlation: X, Y
Pearson correlation of X and Y = 0.96131
interpretation - there is 96 % relation between variable x and Y .
......................................................................................Best of Luck .................................................................
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