Consider the following logistic regression model with known values of the parameters. log(p(x)/(1-p(x))) = -0.73 + 4.76x1 + 0.89x2 p(x) = P[Y = 1 | X = x] = P[Y = 1 | X1 = x1, X2 = x2] Use this model to do the following: (a) Calculate P[Y = 1 | X = x] when x1 = -0.7 and x2 = 0.92. (b) Calculate P[Y = 1 | X = x] when x1 = 0.21 and x2 = -0.58. (c) Calculate P[Y = 0 | X = x] when x1 = 0.03 and x2 = 0.27. (d) Calculate P[Y = 0 | X = x] when x1 = -0.31 and x2 = -0.17.
Added by Josep C.
Close
Step 1
7 and X2 = 0.92. Substitute X1 = -0.7 and X2 = 0.92 into the logistic regression equation: \[ P[Y = 1 | X = c] = \frac{e^{-0.73 + 4.76(-0.7) + 0.89(0.92)}}{1 + e^{-0.73 + 4.76(-0.7) + 0.89(0.92)}} \] \[ P[Y = 1 | X = c] = \frac{e^{-3.2432}}{1 + e^{-3.2432}} Show more…
Show all steps
Your feedback will help us improve your experience
Adi S and 93 other Intro Stats / AP Statistics educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
The following table contains the parameter estimates of the linear probability regression model and the logistic regression model. When considering a binary response variable y and two predictor variables, x1 and x2, what is the predicted probability implied by the logistic regression model for x1 = 2 with x2 = 15? (Hint: for logit, the model is Å· = exp(b0+ b1x1 + b2x2)/(1 + exp(b0 + b1x1 + b2x2)).) Variable Linear Probability Logistic Intercept -0.56 -3.80 x1 0.51 1.47 x2 -0.02 -0.16 Multiple Choice 0.006 0.037 -5.160 0.005 The following table contains the parameter estimates of the linear probability regression model and the logistic regression model. When considering a binary response variable y and two predictor variables, x1 and x2, what is the estimated linear probability implied by the logistic probability regression model for x1 = 3 with x2 = 9? Variable Linear Probability Logistic Intercept -0.68 -1.26 x1 0.50 0.86 x2 -0.02 -0.10 Multiple Choice 1.87 0.35 0.64 -0.87
Kumar A.
Sri K.
The following regression equation is estimated as a production function for
Shaiju T.
Recommended Textbooks
Elementary Statistics a Step by Step Approach
The Practice of Statistics for AP
Introductory Statistics
Transcript
18,000,000+
Students on Numerade
Trusted by students at 8,000+ universities
Watch the video solution with this free unlock.
EMAIL
PASSWORD