Suppose the probability r(z) of reaching a target (such as getting a ball between goal posts) as a function of distance x (in metres) from the target is well-fitted by a logistic regression equation with log(r(z)/1 - (z)) = 6.4 - 0.13z Please answer below to 3 significant digits. Part a) For this prediction model, what is the probability of reaching the target from a distance of 35 metres. Part b) At what distance is the probability of reaching the target equal to 0.6?

Write the multiple regression equation for miles per gallon as the response variable. How might the car rental company use this model?

An investigator modeled the log-odds of getting stomach cancer as a function of number of servings of vegetables per week and the number of servings of red mean per week using logistic regression. The odds that a person gets stomach cancer if they have 4 servings of red meat a week are 1.2 times the odds of cancer for someone who has 3 servings of red meat a week.  Suppose the fitted regression model is given as log-odds = -6 + 0.182 M – 0.105 V, where M = #servings of red meat per week and V = #servings of vegetables per week. What is the odds ratio representing the change in odds for an increase in one serving of vegetables? Give the answer to three decimal places.

Q2 (3 points) Answer the following questions. (1) Given the success probability of an event is p, write down the odds ratio and logit of the event. (2) If Y is a categorical variable with three levels ("A", "B" and "C") and X is the predictor, write down the equations of the multinomial logistic regression of Y ~ X (with intercept) with "A" as the base level. Please clearly define the notations (e.g. conditional probability). (3) For linear model Y₁ = 30+ B₁X+++, write down the first order autocorrelation structure. Please clearly define the notations.

Data was gathered from a random sample of young mothers between the ages of 15 and 19 years, and the relationship between the mother's age (measured in years) and the baby's birth weight (measured in grams) was observed to be linear, with r= 0.88. Further, the regression equation to predict a baby's birth welght based on the mother's age was found to be: Predicted birth weight = -1163.45 + 245.15(age). Based on this information, which one of the following statements is incorrect? O The predicted birth weight for a baby whose mother is 15 years old is 4840.7 grams. O If weight was measured in pounds instead of grams, the value of rwould still be 0.88. O If we switch the variables so that age is the response variable and birth weight is the explanatory variable, r would still be 0,88. O If a mother's age is 25 years, we would not want to use the regression equation to predict the baby's birth weight since this would be considered extrapolation. O Becauseris 0.88, we would consider the…

Suppose you ran a regression of AGE predicting INCOME (thousands of dollars). If your estimated line was INCOME = -1.5 + 1.2*AGE + ε, how much more income do you expect to make for every two years you age? (Express your answer in thousands of dollars.)

Calculate the estimate of σε​ What is the estimated resting heart rate for someone who is a smoker (Smoke=1) and exercises 1 hour a day (Exercise=1)?

Data is collected on the distance of several hikes (in miles), along with the amount of time (in minutes) the hike is expected to take. All hikes in the data set are between 0.5 miles and 10 miles long, and the relationship between distance and time is linear and strong.   The regression equation to predict time based on distance is as follows:  Predicted time =   –266 + 31.48 (distance).  Suppose we want to use the regression equation to predict the time it takes to complete a particular hike.  For which one of the following distances would using the regression equation result in extrapolation?     1 mile 4.5 miles 6.8 miles 9 miles None of the above distances would result in extrapolation.

Suppose a data set of 200 observations (n = 200) was analyzed using OLS to examine the relationship between CEO salary and various measures of firm performance. The regression results are as follows, with standard errors in parentheses: logy = 5 + 0.2logx₁0.03x₂ +0.002x3 (0.2) (0.04) (0.004) where? (0.009) y = CEO salary in thousands of dollars X₁ = annual firm sales X₂ = percentage of sales lost to competitors X3 = return on stock in percent R² = 0.290 Suppose you want to test the null hypothesis that percentage of sales lost to competitors has no ceteris paribus effect on the salaries of CEOS. For the one-sided alternative hypothesis ß₂ < 0 and 1% rejection rule (i.e., at the 1% level), you would_ the null hypothesis that ß₂ = 0.

A researcher is attempting to explore the relationship between study duration per day (0 - 8) and the passing of the science course (Pass=1, Fail=0). For this purpose, a sample of 36 students from Alabama University are chosen.  Summary of the logistic regression model has been included. Please help me understand and choose from the following below, which is the correct representation of the related logistic regression model in the summary photo attached.    - PASS = 0.57 + 3.69 X SDURATION - PASS= 3.69 +0.57 X SDURATION - PASS/FAIL=3.69 + 0.57 x SDURATION - P(PASS/F(FAIL)=3.69+ 0.57 X SDURATION - PASS/FAIL= 0.57 + 3.69 x SDURATION - ln{P(PASS/F(FAIL)}=0.57 + 3.69 X SDURATION - ln{P(PASS/F(FAIL)}= 3.69+ 0.57 X SDURATION