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Given the data of the dependence of Y on four independent variables, I have run 3 different regression analyses. Determine the listed items. X1 X2
Given the data of the dependence of Y on four independent variables, I have run 3 different regression analyses. Determine the listed items.
X1 | X2 | X3 | X4 | Y |
4 | 1 | 1 | 3 | 0.73 |
5 | 3 | 1 | 4 | 3.2 |
3 | 3 | 3 | 4 | 2.68 |
6 | 2 | 1 | 2 | 2.17 |
7 | 1 | 4 | 2 | 2.4 |
5 | 4 | 1 | 2 | 3.74 |
9 | 1 | 3 | 2 | 2.93 |
8 | 1 | 2 | 1 | 2.04 |
6 | 3 | 5 | 4 | 3.44 |
8 | 1 | 2 | 4 | 2.43 |
8 | 2 | 3 | 4 | 2.63 |
9 | 2 | 4 | 2 | 4.11 |
6 | 4 | 3 | 7 | 4.65 |
9 | 1 | 4 | 4 | 2.63 |
4 | 2 | 5 | 6 | 2.29 |
4 | 3 | 2 | 3 | 2.71 |
9 | 2 | 2 | 2 | 3.26 |
9 | 4 | 4 | 2 | 5.48 |
7 | 2 | 5 | 4 | 2.94 |
9 | 4 | 4 | 10 | 5.9 |
SUMMARY OUTPUT | |
Regression Statistics | |
Multiple R | 0.977642097 |
R Square | 0.95578407 |
Adjusted R Square | 0.943993155 |
Standard Error | 0.284748587 |
Observations | 20 |
ANOVA | |||||
df | SS | MS | F | Significance F | |
Regression | 4 | 26.29029363 | 6.572573408 | 81.06106205 | 5.7E-10 |
Residual | 15 | 1.216226368 | 0.081081758 | ||
Total | 19 | 27.50652 |
Coefficients | Standard Error | t Stat | P-value | Lower 95% | Upper 95% | Lower 85.0% | Upper 85.0% | |
Intercept | -1.67546899 | 0.298891441 | -5.605610458 | 5.0128E-05 | -2.31254 | -1.038396963 | -2.12895544 | -1.221982536 |
X1 | 0.332607544 | 0.034256725 | 9.709262759 | 7.35655E-08 | 0.25959 | 0.405624025 | 0.28063228 | 0.384582805 |
X2 | 0.906460659 | 0.065587491 | 13.82063324 | 6.13218E-10 | 0.76666 | 1.046257087 | 0.80694948 | 1.005971835 |
X3 | 0.107717232 | 0.052864264 | 2.037619073 | 0.059628999 | -0.00496 | 0.220394743 | 0.02751009 | 0.187924372 |
X4 | 0.040484089 | 0.036951567 | 1.095598711 | 0.290534144 | -0.03828 | 0.119244489 | -0.01557986 | 0.096548039 |
RESIDUAL OUTPUT | |||
Observation | Predicted Y | Residuals | Standard Residuals |
1 | 0.790591342 | -0.060591342 | -0.239486019 |
2 | 2.976604292 | 0.223395708 | 0.882966889 |
3 | 2.526823669 | 0.153176331 | 0.605426261 |
4 | 2.321783 | -0.151783 | -0.599919148 |
5 | 2.071081581 | 0.328918419 | 1.300043208 |
6 | 3.802096773 | -0.062096773 | -0.245436204 |
7 | 2.628579437 | 0.301420563 | 1.191358507 |
8 | 2.147770572 | -0.107770572 | -0.425960943 |
9 | 3.740080765 | -0.300080765 | -1.186062982 |
10 | 2.269222838 | 0.160777162 | 0.635468388 |
11 | 3.283400729 | -0.653400729 | -2.582552791 |
12 | 3.642757328 | 0.467242672 | 1.846766943 |
13 | 4.552559226 | 0.097440774 | 0.385132634 |
14 | 2.817264847 | -0.187264847 | -0.740160411 |
15 | 2.249373196 | 0.040626804 | 0.160576596 |
16 | 2.711229892 | -0.001229892 | -0.004861122 |
17 | 3.427322863 | -0.167322863 | -0.661340136 |
18 | 5.455678645 | 0.024321355 | 0.096129649 |
19 | 3.16622765 | -0.22622765 | -0.894160081 |
20 | 5.779551356 | 0.120448644 | 0.476070762 |
Question:
a) 2 most significant variables (in numerical order)
b) t value of the intercept with 3 variables (0.xxx)
c) Best Lower 85% confidence limit of slope of X3 (x.xx)
d) Lower prediction limit of y at x3=5 (x.xx). Use only that variable, alpha =.03
e) Would you drop any data points? Yes or No
f) What is the percentage of variation of y accounted for by the variable X3?
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