Factors influencing the Human Development Index (HDI) using Multiple Linear Regression
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Identified the most crucial factors that influence Human Development Index through regression analysis using Minitab software
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Regression 1 2933 2933.1 21.33 0.000
SBP 1 2933 2933.1 21.33 0.000
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Analysis of Variance
Source DF Adj SS Adj MS F-Value P-Value
Regression 1 4828.5 4828.47 66.81 0.000
SBP 1 4828.5 4828.47 66.81 0.000
Error 27 1951.4 72.27
Lack-of-Fit 20 949.9 47.49 0.33 0.975
Pure Error 7 1001.5 143.07
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S R-sq R-sq(adj) R-sq(pred)
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SBP 0.7502 0.0918 8.17 0.000 1.00
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Age = -59.9 + 0.7502 SBP
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This study examines the relationship between working capital management ratios and profitability. The study analyzes debtors turnover ratio, stock turnover ratio, creditors turnover ratio, working capital turnover ratio, and return on assets using descriptive statistics, correlation, and regression analyses on a company's financial data. The results of the regression model show that the working capital ratios together explain 23.5% of the variation in return on assets. Improving inventory management, accounts receivable collection, payment terms, and overall working capital management can positively impact a firm's profitability.
Durbib- Watson D between 0-2 means there is a positive correlati
Durbib- Watson D between 0-2 means there is a positive correlation at 92% of 1st Order Correlation(1 time unit lag).
The summary shows a linear regression of CO2 emissions vs time. The p-value(<0.05) suggests that the model is significant. The model also defines 68% of the variability in data(R-square=0.6844). The equation for our regression model will be:
CO2 emissions = 0.00002008*Date+0.11162
The residual values doesn’t seem random but normal. We can also see that for higher values of CO2 emissions (>0.5) the variance increases. So, we will check a squared model to see if that explains the data prediction better.
The squared regression shows better R square of 78% and p-values show that Date and Date^2 coefficients are significant but intercept is not. New equation will be:
CO2 emissions = 5.9E-10*(Date^2) +0.0000246*Date-0.009480
Now we will run the time series using ARIMA that includes Auto Regression and Moving Average. To run an ARIMA model we need to define p (lags in Auto Regression), d (non-seasonal difference) and q (lagged forecast errors in Moving Average). These attribute will be defined by checking for seasonality, ACF and PACF plots.
The Autocorrelation check is used to test for white noise. If the p-value is significant, we can say that the data is correlated else the data is independent. Here the tables shows the autocorrelations at different lags and p-values suggest that the data is correlated.
The ACF and PACF plots are used to identify p (lag for auto regression) and seasonality. We can see that ACF plot starts with a positive value and then continues with negative values till 12. But there is no pattern following.
So, we can say that AR is explained very well using lag-1. Also, the PACF plot cuts off at 2. We will iterate through different pdq values and get the best estimates with lowest AIC score.
The pdq (2,1,1) shows better AIC -2426 compared to other pdq values as well as squared regression. The p-value <0.05 also signifies that the parameters we have selected are good. We will predict using these parameters
The distribution of residuals are normal unlike regression and squared regression
The tables show the equation for Autoregression and Moving Average prediction of ARIMA model
This tables shows the forecast of next 12 months of data
Graphical Forecast highlighted by line at the end and connected with the existing data. So this plot shows the complete trend of historical data+predicted data
The last table shows the outliers with row number and values of the observations.
Monday, 21 June 2021 00:08:42 1
Model: MODEL1
Dependent Variable: CO2
Number of Observations Read 1680
Number of Observations Used 1680
Analysis of Variance
Source DF
Sum of
Squares
Mean
Square F Value Pr > F
Model 0 0 . . .
Error 1679 215.11655 0.12812
Corrected Total 1679 215.11655
Root MSE 0.35794 R-Square 0.0000
Dependent Mean 0.03483 Adj R-Sq 0.0000
Coeff Var 1027.75772
Parameter Estimates
Variable D ...
Design and Simulation of a Modified Architecture of Carry Save Adder
This document summarizes a research paper that presents a modified architecture for a carry-save adder. The architecture performs binary addition using a series of XOR, AND, and shift-left operations. A behavioral model was developed in MATLAB to analyze all possible addition combinations for operands up to 15 bits. The model found that the number of shift operations varies from 0 to the number of bits. A mathematical model was derived to predict the average number of shifts for standard operand sizes like 32, 64, or 128 bits. 4-bit synchronous and asynchronous prototypes were designed in Quartus II and simulated to validate the modified adder architecture.
Testing for normality
This document discusses methods for testing whether a data set is normally distributed. It describes both graphical and statistical tests for normality, including Q-Q plots and the Kolmogorov-Smirnov, Shapiro-Wilk, and Lilliefors tests. It then provides a detailed example of how to perform the Kolmogorov-Smirnov test for normality on a set of height data.
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Factors influencing the Human Development Index (HDI) using Multiple Linear Regression
- 1. Factors influencing the Human Development Index (HDI) using Multiple linear regression ADITYA PANUGANTI 1202062944 Industrial Engineering Year of data: 2008 Source: UN Development Programme Database
- 2. Objective and Dataset description To find which of the following variables have an effect on the Human Development Index (HDI)
- 3. Fitting the full model without interaction terms The regression equation for full model is y = 0.0596 + 0.00440 LIF + 0.000007 GDP - 0.000748 GRO + 0.0158 SCH + 0.0080 GEN+ 0.0159 EXP - 0.000004 GNI + 0.000003 MAT - 0.000051 HOM - 0.000540 MOR+ 0.000176 LIT - 0.0185 DEP + 0.0023 CON1 - 0.0117 CON2 - 0.0100 CON3+ 0.00431 CON4 - 0.0268 CON5 Difficult to interpret the coefficients of the above regression equation. Hence standardized the regression coefficients using Unit Normal scaling
- 4. Fitting the full model after Standardization The regression equation is y = 0.684 + 0.0404 LIF + 0.100 GDP - 0.0117 GRO + 0.0408 SCH + 0.00136 GEN+ 0.0443 EXP - 0.0627 GNI + 0.00089 MAT - 0.00068 HOM - 0.0196 MOR+ 0.00259 LIT - 0.0185 DEP + 0.0023 CON1 - 0.0117 CON2 - 0.0100 CON3+ 0.00431 CON4 - 0.0268 CON5 Model Statistics: R-Sq = 98.5% R-Sq(adj) = 98.2% Analysis of Variance (ANOVA) Source DF SS MS F P Regression 17 2.21784 0.13046 325.49 0.000 Residual Error 84 0.03367 0.00040 Total 101 2.25150
- 7. Indicator Interactions Considered interaction terms of DEP and other numerical variables. 24 variables in all including all the interaction terms S = 0.0220704 R-Sq = 98.3% R-Sq(adj) = 97.8%; R-Sq(pred) = 96.80% Residual plots:
- 8. Outliers and Influential points
- 9. Other outliers in graph Fitting each of the datapoints 45, 50, 80 and checking if there is any changes in summary stats These points are not contributing to any leverage, nor being influential; except for the fact that they are outliers; also R-sq not changing much, therefore we are leaving them in the model.
- 12. Residual plots after transformation Can find some outliers in the Normal probability plot
- 13. Outliers and Influential points
- 14. Residual plots after taking off the outliers and influential points No need for any transformation, Box-Cox suggests λ = 1
- 15. Variable selection and Model building
- 16. Fit the selected model Regression equation: y2= 0.476 - 0.0164 GEN + 0.0403 GRO + 0.0422 LIF + 0.0557 GDP + 0.0449 SCH - 0.0181 CON2 - 0.0388 MOR + 0.0523 GDP_D + 0.0289 CON5 + 0.0412 MOR_D - 0.0476 HOM_D Detected Multicollinearity using Principal component analysis condition number = 134.837 (>100, Moderate Multicollinearity) Linear dependency equation: 0.107GRO+0.337LIF+0.798MOR-0.467MOR_D (dependency between the variables in the equation) Using correlation matrix found that the variable MOR has large correlation with LIF and MOR_D. Dropping MOR removed multicollinearity from model (condition number = 39.04617 (<100, No multicollinearity)
- 19. Model validation Considered 118 countries for modelling 102 Estimation data and 16 prediction data
- 20. Conclusion The reduced model has a better R-sq than the actual model and most of the variables are significant (low p-value) in the model. The following variables were found to be significant Gender inequality index Combined gross enrolment Life expectancy at birth GDP Mean schooling years Countries in continent 2 GDP& intensity of deprivation Under 5 mortality rate& intensity of deprivation Homicide rate& intensity of deprivation
- 21. Possible improvements More datapoints Ridge regression to eliminate multicollinearity Robust regression – to add more weight to the datapoints and retain them in the model.