Regression-logistic, multivariate, linear

Paper, Order, or Assignment Requirements

it is a regression statistics at master level.

Assignment 4

  1. A study was conducted to investigate the effects of gender (0=Male, 1=Female), rank (assistant, associate or full professor) and years at current rank on salary.
    • State the regression equation. Define all the variables.
    • The following table summarizes the fit of the three predictors. Use the results of this table to draw conclusions to four hypotheses related to the regression
Sum Sq Df F value Pr(>F)
sex 2304648 1 0.394333 0.53307
rank 6.34E+08 2 54.24016 <0.0001
yearsRank 1.57E+08 1 26.89455 <0.0001
Residuals 2.75E+08 47    

 

  • The following table is of the regression coefficients. Interpret each of the regression coefficients (comment on both the value and the associated p-value)
Estimate Std. Error t value Pr(>|t|)
(Intercept) 25390.65      
sex female 524.1492 834.6869 0.627959 0.53307
rank assistant -9483.84 912.7945 -10.3899 <0.0001
rank associate -5109.93 887.1232 -5.76011 0.1285
yearsRank 390.9358 75.38298 5.185995 <0.0001

 

  • What is the predicted salary for an assistant female professor with 7 years of experience at her current rank?
  1. A study was conducted to determine if age and treatment (two treatments, A and B) are significant predictors of dying from ovarian cancer (binary outcome, died or survived).
    • State the regression equation, define all variables.
    • The following table lists the model fit statistics. Use the results of this table to draw conclusions to three hypotheses related to the regression
LR Chisq Df Pr(>Chisq)
Treatment 0.987023 1 0.320471
age 8.050765 1 0.004548

 

  • The following table lists the regression coefficients. Interpret each of the regression coefficients (comment on both the value and the associated p-value)
Estimate Std. Error t value Pr(>|t|)
(Intercept) -0.69838      
Treatment B -0.1758 0.176953 -0.99349 0.330809
age 0.025347 0.008933 2.837387 0.009331

 

  • What is the probability of a 56 year on treatment dying from their ovarian cancer?
  1. For the ovarian cancer example in question 5, we have survival times for both subjects that did and did not experience the event. Along with age and treatment, there are independent variables measuring presence of residual disease and ECOG score (1=high, 0=normal).
    • The following figure presents the KM curves comparing treatment vs no treatment. Interpret the KM curves, and use the test statistic to determine if the difference between the two groups is significant.
    • The following table presents the regression coefficients and standard errors for those coefficients. Calculate and interpret the p-values and RR for each of the regression coefficients.
  Coefficient SE Test Statistic P-Value RR
Treatment -0.8146 0.6342      
Age 0.1470 0.0493      
ECOG 0.1032 0.6064      

 

 

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