Multiple Correlation Coefficient

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James Algina - One of the best experts on this subject based on the ideXlab platform.

  • confidence intervals for squared semipartial Correlation Coefficients the effect of nonnormality
    Educational and Psychological Measurement, 2010
    Co-Authors: James Algina, H. J. Keselman, Randall D Penfield
    Abstract:

    The increase in the squared Multiple Correlation Coefficient (ΔR2) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. Algina, Keselman, and Penfield found that intervals based on asymptotic principles were typically very inaccurate, even though the sample size was quite large (i.e., larger than 200). However, they also reported that probability coverage for the confidence intervals based on a bootstrap method was typically quite accurate, and moreover, this accuracy was obtained with relatively small sample sizes with six or fewer predictors. They further speculated that nonnormality would likely affect the accuracy of interval coverage. In the present study, the authors investigated the accuracy of coverage probability for confidence intervals obtained by using asymptotic and percentile bootstrap methodology when either predictors, residuals, or both are nonnormal. Coverage probability for asymptotic confidence intervals is poor, but adequ...

  • Note on a Confidence Interval for the Squared Semipartial Correlation Coefficient
    Educational and Psychological Measurement, 2008
    Co-Authors: James Algina, H. J. Keselman, Randall J. Penfield
    Abstract:

    A squared semipartial Correlation Coefficient (ΔR2) is the increase in the squared Multiple Correlation Coefficient that occurs when a predictor is added to a Multiple regression model. Prior research has shown that coverage probability for a confidence interval constructed by using a modified percentile bootstrap method with ΔR2 was generally good with sample sizes that should not be too challenging for educational and psychological researchers. However, that research was limited to values of Δρ2 = .00 or Δρ2 ≥ .05. The present research investigates coverage probability when .01 ≤ Δρ2 ≤ .04 and shows that the modified percentile bootstrap typically results in coverage probability in the [.925, .975] interval for a 95% confidence interval, provided the sample size is at least 50 if the number of predictors in the model with more predictors (i.e., the full model) is four or smaller, at least 150 if the number of predictors in the full model is five or six, and at least 200 and preferably 250 if the number ...

  • invited articles confidence intervals for the squared Multiple semipartial Correlation Coefficient
    2008
    Co-Authors: James Algina, H. J. Keselman, Randall D Penfield
    Abstract:

    The squared Multiple semipartial Correlation Coefficient is the increase in the squared Multiple Correlation Coefficient that occurs when two or more predictors are added to a Multiple regression model. Coverage probability was investigated for two variations of each of three methods for setting confidence intervals for the population squared Multiple semipartial Correlation Coefficient. Results indicated that the procedure that provides coverage probability in the [ ] .925, .975 interval for a 95% confidence interval depends primarily on the number of added predictors. Guidelines for selecting a procedure are presented.

  • confidence intervals for an effect size measure in Multiple linear regression
    Educational and Psychological Measurement, 2007
    Co-Authors: James Algina, H. J. Keselman, Randall J. Penfield
    Abstract:

    The increase in the squared Multiple Correlation Coefficient (ΔR 2) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. The coverage probability that an asymptotic and percentile bootstrap confidence interval includes Δρ2 was investigated. As expected, coverage probability for the asymptotic confidence interval was often inadequate (outside the interval .925 to .975 for a 95% confidence interval), even when sample size was quite large (i.e., 200). However, adequate coverage probability for the confidence interval based on a bootstrap interval could typically be obtained with a sample size of 200 or less, and moreover, this accuracy was obtained with relatively small sample sizes (100 or less) with six or fewer predictors.

  • sample sizes for confidence intervals on the increase in the squared Multiple Correlation Coefficient
    Educational and Psychological Measurement, 2001
    Co-Authors: James Algina, Bradley C Moulder
    Abstract:

    The increase in the squared Multiple Correlation Coefficient (δR2) associated with a variable in a regression equation is a commonly used measure of importance in regression analysis. The probabili...

Ram Sarup Singh - One of the best experts on this subject based on the ideXlab platform.

  • statistical optimization of solid state fermentation for the production of fungal inulinase from apple pomace
    Bioresource Technology Reports, 2020
    Co-Authors: Ram Sarup Singh, Kanika Chauhan, Karminder Kaur, Ashok Pandey
    Abstract:

    Abstract The present work was designed to determine the suitability of apple pomace for inulinase production from Mucor circinelloides by solid-state fermentation (SSF). Central composite rotatable deign (CCRD) matrix (15 runs) of RSM was experimentally executed to investigate the influence of moisture, pH and fermentation time on fungal inulinase production from apple pomace by SSF. SSFs were performed at flask-level at 30 °C. Under optimized conditions viz., moisture 83.5%, pH 6.4 and fermentation time 5.8 days, maximum inulinase production was 411.3 IU/gds. Coefficient of variation (CV%) 0.17 indicates the lowest deviations between the experimental and predicted values. Multiple Correlation Coefficient (R2) was calculated to be 1.00 for inulinase production, which signifies the good Correlation between the experimental and predicted results. Model's higher F-value 94,051.9 and “Lack-of-Fit” F-value 0.43 also verifies the authenticity of the quadratic model. The present article highlights the applicability of apple pomace as potent substrate for inulinase production by M. circinelloides.

  • response surface optimization of solid state fermentation for inulinase production from penicillium oxalicum using corn bran
    Journal of Food Science and Technology-mysore, 2018
    Co-Authors: Ram Sarup Singh, Kanika Chauhan, Arju Jindal
    Abstract:

    Response surface methodology has been implemented for the utilization of corn bran for inulinase production by Penicillium oxalicum. CCRD of RSM with 15 runs was practiced to optimize three independent variables: moisture (70–90%), incubation time (4–8 days) and pH (5–8). However, other media constituents viz. inulin (1%), NaNO3 (0.2%), NH4H2PO4 (0.2%), KH2PO4 (0.2%), MgSO4·7H2O (0.05%) and FeSO4·7H2O (0.001%) were kept constant during solid state fermentations. Solid state fermentations were carried out at 30 °C at flask-level. A substantial inulinase production (77.95 IU/gds) was obtained under the optimized conditions i.e., moisture (80%), incubation time (6.0 days) and pH (6.5). Multiple Correlation Coefficient ‘R2’ for inulinase production was 1.00, which justifies good agreement between experimental and predicted values. Besides, ‘R2’ value close to one, also authenticates the validity of the model. The experimentation carried out at laboratory scale shown corn bran a good substrate for inulinase production by P. oxalicum.

  • response surface optimization of the critical medium components for pullulan production by aureobasidium pullulans fb 1
    Applied Biochemistry and Biotechnology, 2009
    Co-Authors: Ram Sarup Singh, Harpreet Singh, Gaganpreet K Saini
    Abstract:

    Culture conditions for pullulan production by Aureobasidium pullulans were optimized using response surface methodology at shake flask level without pH control. In the present investigation, a five-level with five-factor central composite rotatable design of experiments was employed to optimize the levels of five factors significantly affecting the pullulan production, biomass production, and sugar utilization in submerged cultivation. The selected factors included concentration of sucrose, ammonium sulphate, yeast extract, dipotassium hydrogen phosphate, and sodium chloride. Using this methodology, the optimal values for concentration of sucrose, ammonium sulphate, yeast extract, dipotassium hydrogen phosphate, and sodium chloride were 5.31%, 0.11%, 0.07%, 0.05%, and 0.15% (w/v), respectively. This optimized medium has projected a theoretically production of pullulan of 4.44%, biomass yield of 1.03%, and sugar utilization of 97.12%. The Multiple Correlation Coefficient ‘R’ was 0.9976, 0.9761 and 0.9919 for pullulan production, biomass production, and sugar utilization, respectively. The value of R being very close to one justifies an excellent Correlation between the predicted and the experimental data.

K Krishnamoorthy - One of the best experts on this subject based on the ideXlab platform.

  • sample size calculation for estimating or testing a nonzero squared Multiple Correlation Coefficient
    Multivariate Behavioral Research, 2008
    Co-Authors: K Krishnamoorthy
    Abstract:

    The problems of hypothesis testing and interval estimation of the squared Multiple Correlation Coefficient of a multivariate normal distribution are considered. It is shown that available one-sided tests are uniformly most powerful, and the one-sided confidence intervals are uniformly most accurate. An exact method of calculating sample size to carry out one-sided tests (null hypothesis may involve a nonzero value for the Multiple Correlation Coefficient) to attain a specified power is given. Sample size calculation for computing confidence intervals for the squared Multiple Correlation Coefficient with a specified expected width is also provided. Sample sizes for powers and confidence intervals are tabulated for a wide range of parameter configurations and dimensions. The results are illustrated using the empirical data from Timm (1975) that related scores from the Peabody Picture Vocabulary Test to four proficiency measures.

  • computing discrete mixtures of continuous distributions noncentral chisquare noncentral t and the distribution of the square of the sample Multiple Correlation Coefficient
    Computational Statistics & Data Analysis, 2003
    Co-Authors: Denise Benton, K Krishnamoorthy
    Abstract:

    In this article, we address the problem of computing the distribution functions that can be expressed as discrete mixtures of continuous distributions. Examples include noncentral chisquare, noncentral beta, noncentral F, noncentral t, and the distribution of squared sample Multiple Correlation. We illustrate the need for improved algorithms by pointing out situations where existing algorithms fail to compute meaningful values of the cumulative distribution functions (cdf) under study. To address this problem we recommend an approach that can be easily incorporated to improve the existing algorithms. For the distributions of the squared sample Multiple Correlation Coefficient, noncentral t, and noncentral chisquare, we apply the approach and give a detailed explanation of computing the cdf values. We present results of comparison studies carried out to validate the calculated values and computational times of our suggested approach. Finally, we give the algorithms for computing the distributions of the squared sample Multiple Correlation Coefficient, noncentral t, and noncentral chisquare so that they can be coded in any desired computer language.

D Najarzadeh - One of the best experts on this subject based on the ideXlab platform.

Arju Jindal - One of the best experts on this subject based on the ideXlab platform.

  • response surface optimization of solid state fermentation for inulinase production from penicillium oxalicum using corn bran
    Journal of Food Science and Technology-mysore, 2018
    Co-Authors: Ram Sarup Singh, Kanika Chauhan, Arju Jindal
    Abstract:

    Response surface methodology has been implemented for the utilization of corn bran for inulinase production by Penicillium oxalicum. CCRD of RSM with 15 runs was practiced to optimize three independent variables: moisture (70–90%), incubation time (4–8 days) and pH (5–8). However, other media constituents viz. inulin (1%), NaNO3 (0.2%), NH4H2PO4 (0.2%), KH2PO4 (0.2%), MgSO4·7H2O (0.05%) and FeSO4·7H2O (0.001%) were kept constant during solid state fermentations. Solid state fermentations were carried out at 30 °C at flask-level. A substantial inulinase production (77.95 IU/gds) was obtained under the optimized conditions i.e., moisture (80%), incubation time (6.0 days) and pH (6.5). Multiple Correlation Coefficient ‘R2’ for inulinase production was 1.00, which justifies good agreement between experimental and predicted values. Besides, ‘R2’ value close to one, also authenticates the validity of the model. The experimentation carried out at laboratory scale shown corn bran a good substrate for inulinase production by P. oxalicum.