Multiple Linear Regression - Estimated Regression Equation
Calculation[t] = + 55.3143 + 0.248321Algebraic_Reasoning[t] + 0.193203Graphical_Interpretation[t] + 0.102884Proportionality_and_Ratio[t] + 0.00225489Probability_and_Sampling[t] -0.0272716year[t] + 0.0383029group[t] + 0.031862gender[t] + e[t]


Multiple Linear Regression - Ordinary Least Squares
VariableParameterS.D.T-STAT
H0: parameter = 0		2-tail p-value1-tail p-value
(Intercept)+55.31 37.66+1.4690e+00 0.1431 0.07153
Algebraic_Reasoning+0.2483 0.05584+4.4470e+00 1.274e-05 6.369e-06
Graphical_Interpretation+0.1932 0.04363+4.4280e+00 1.382e-05 6.908e-06
Proportionality_and_Ratio+0.1029 0.02765+3.7200e+00 0.000242 0.000121
Probability_and_Sampling+0.002255 0.02721+8.2880e-02 0.934 0.467
year-0.02727 0.01872-1.4570e+00 0.1464 0.07319
group+0.0383 0.01859+2.0600e+00 0.04032 0.02016
gender+0.03186 0.01939+1.6430e+00 0.1016 0.0508


Multiple Linear Regression - Regression Statistics
Multiple R 0.5682
R-squared 0.3228
Adjusted R-squared 0.3052
F-TEST (value) 18.39
F-TEST (DF numerator)7
F-TEST (DF denominator)270
p-value 0
Multiple Linear Regression - Residual Statistics
Residual Standard Deviation 0.1502
Sum Squared Residuals 6.095


Menu of Residual Diagnostics
DescriptionLink
HistogramCompute
Central TendencyCompute
QQ PlotCompute
Kernel Density PlotCompute
Skewness/Kurtosis TestCompute
Skewness-Kurtosis PlotCompute
Harrell-Davis PlotCompute
Bootstrap Plot -- Central TendencyCompute
Blocked Bootstrap Plot -- Central TendencyCompute
(Partial) Autocorrelation PlotCompute
Spectral AnalysisCompute
Tukey lambda PPCC PlotCompute
Box-Cox Normality PlotCompute
Summary StatisticsCompute


Ramsey RESET F-Test for powers (2 and 3) of fitted values
> reset_test_fitted
	RESET test
data:  mylm
RESET = 15.84, df1 = 2, df2 = 268, p-value = 3.147e-07
Ramsey RESET F-Test for powers (2 and 3) of regressors
> reset_test_regressors
	RESET test
data:  mylm
RESET = 1.6699, df1 = 14, df2 = 256, p-value = 0.06209
Ramsey RESET F-Test for powers (2 and 3) of principal components
> reset_test_principal_components
	RESET test
data:  mylm
RESET = 1.7475, df1 = 2, df2 = 268, p-value = 0.1762


Variance Inflation Factors (Multicollinearity)
> vif
      Algebraic_Reasoning  Graphical_Interpretation Proportionality_and_Ratio 
                 1.424253                  1.357782                  1.171012 
 Probability_and_Sampling                      year                     group 
                 1.241136                  1.038467                  1.063476 
                   gender 
                 1.136489