In the simple linear regression equation ŷ = bo + b₁x, how is b₁ interpreted? it is the change in x that occurs with a one-unit change in It is the estimated value of ŷ when x = 0 O It is the change in ŷ that occurs when bo increases it is the change in ŷ that occurs with a one-unit change in x
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- You run a logistic regression model in R using the glm() function. The dependent variable is the factor variable Y and independent variables are X1 and X2 (in other words, the formula is Y~X1+X2). In the model output, the coefficient of the constant term is a0, the coefficient of X1 is a1, and the coefficient of X2 is a2. Assuming a cutoff = 0.5, which of the following defines the equation of a decision boundary? a0 + a1X1 + a2X2 = 0.5 exp(-(a0 + a1X1 + a2X2)) = 0 a0 + a1X1 + a2X2 = 0 O exp(-(a0 + a1X1 + a2X2)) = 0.5In bivariate regression, the regression coefficient will be equal to rXY when:We create a simple regression model and call the fit function as follows: Im=LinearRegression() Im.fit(X,Y) in a multilinear model we proceed in the same way: mlm=LinearRegression() mlm.fit(Z,Y) How does the linear regression model knows if we are doing a simple or multiple linear regression? Answer:
- If we build a simple linear regression model: y = =w₁x +wo + € to predict how daily happiness (y) increases with chocolate intake per day in grams (x), where e corresponds to a random noise variable describing the error in our predictions. What can we interpret wo as? The decrease in happiness per gram of chocolate The expected happiness of a day without chocolate The increase in happiness per gram of chocolate The amount of chocolate required to make anyone happyThe temperature T (in °C) and length L (in mm) of a heated rod is given in the following table, if: L = a + bT where, a and b are constants, find the best value of constants for each data by using linear regression fit. L (mm) 20 30 40 50 60 70 T(°C) 600.1 600.4 600.6 600.7 600.9 601.0We predict the amount that a car is worth by it's age (in years). We run a linear regression and obtain the following parameter estimates. b0 = 50,000 b1 = -1,500 How much would you predict a car aged 25 years is worth? Answer:
- What is the final equation for Simple Linear regression if we have Pas an independent variable, Q as a dependent variable, a is the intercept, and m is the regression coefficient? O a. P=a+mQ O b. Q=a+mP O . Q=am+ P O d. Q=aP+m ge Next paI estimate the following regression that relates an individual's test score (from 0 to 100) to their homework grade (also zero to 100): Test Scorei = BoB₁ HW Gradei I find that the intercept is equal to 50. What is difference in predicted test scores for an individual that scored a 90 on homework vs. an individual that scored 95 on the homework?Listed below are systolic blood pressure measurements (in mm Hg) obtained from the same woman. Find the regression equation, letting the right arm blood pressure be the predictor (x) variable. Find the best predicted systolic blood pressure in the left arm given that the systolic blood pressure in the right arm is 80 mm Hg. Use a significance level of 0.05. Right Arm 103 102 94 79 79 O Left Arm 176 171 143 145 145 E Click the icon to view the critical values of the Pearson correlation coefficient r The regression equation is y = 53.4 + 1.1 x. (Round to one decimal place as needed.) Given that the systolic blood pressure in the right arm is 80 mm Hg, the best predicted systolic blood pressure in the left arm is (Round to one decimal place as needed.) mm Hg.
- I estimate the following regression that relates an individual's test score (from 0 to 100) to their homework grade (also zero to 100): Test Score = BoB₁ HW Gradei I find that the slope coefficient is equal to 0.5. What is difference in predicted test scores for an individual that scored a 90 on homework vs. an individual that scored 95 on the homework?You have built a classification model to predict if a patient will be readmitted within 30 days of discharge from the hospital. When you examine the ROC curve you find that it essentially coincides with the central diagonal of the curve. Based on this, which of the following can you infer: Your model performs about as good as random guessing Your model performs much worse than random guessing Your model performs much better than random guessing"When conducting a binary regression with a skewed predictor, it is often easiest to assess the need for x and log(x) by including them both in the model so that their relative contributions can be assessed directly." Show that indeed the log odds are a function of x and log(x) for the gamma distribution.