Q4 (8 points) One would like to study the relationship between the sepal length, sepal width and the species of iris using logistic regression. There are two species, setosa(-1), versicolor(=0). The output is given in the table below. Coefficients: Estimate Std. Error z value Pr(>Izl) (Intercept) -18.3069 4.5467 -4.026 5.66e-05 *** Sepal. Length -0.8447 Sepal.Width 7.8053 0.2848 1.6568 4.711 2.47e-06 *** Signif. codes: 0*** 0.001 *** 0.01 * 0.05 0.1'1 (Dispersion parameter for binomial family taken to be 1) Null deviance: 138.629 on 99 Residual deviance: 59.734 on 97 AIC: 65.734 degrees of freedom degrees of freedom Number of Fisher Scoring iterations: 6 (a) Interpret sepal.Length based on the estimated value and test the hypothesis Ho: Sepal.Length = 0 against H₁ Sepal Length 0 at the significance level 0.05. (b) Calculate the R-square and the maximum likelihood (L(B)). (c) Use the G-statistic to test the hypothesis Ho ẞSepal.Length 0.05. Sepal. Width 0 at the significance level ẞSepal.Width (d) The following is a testing set of 10 new observations. Based on part (a), calculate the estimated probabilities of being setosa for the testing set. If the cutoff values are chosen at 0.4, what is the proportion of correct classification? Sepal. Length Sepal. Width Species.type 5.36 3.5 1 6.67 3.0 1 4.93 3.2 1 5.24 3.1 1 6.43 3.6 1 9.73 3.2 0 8.09 3.2 0 9.38 3.1 0 5.85 2.3 0 7.01 2.8 0

A hydrologist is interested in studying the influence of rainfall on runoff in a drainage basin. Rainfall and runoff are measured during 20 rainfall events. Model the relationship. What are the variables and the type of measurement for these variables? slope (numerical) and itercept (numerical) dependent variable (nominal) and independent vatiable (nominal) Rainfall (total mm) and Runoff (liters/36 hours) geographic location (lat/long), area of watershed (hectares), and substrate type (rock/soil/vegitation) rainfall (numerical) and runoff (numerical)

The data show the bug chirps per minute at different temperatures. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best-predicted temperature for a time when a bug is chirping at the rate of 3000chirps per minute. Use a significance level of 0.05. What is wrong with this predicted​ value?   Chirps in 1 min 1004 952 1237 1116 1177 1249   Temperature ​(°​F) 83.1 76 95.1 87.5 92.1 88.4 What is the regression​ equation?   (^ over y)=_____+_____x ​(Round the​ x-coefficient to four decimal places as needed. Round the constant to two decimal places as​ needed.)   What is the best-predicted temperature for a time when a bug is chirping at the rate of 3000chirps per​ minute?   The best-predicted temperature when a bug is chirping at 3000 chirps per minute is ____°F. ​(Round to one decimal place as​ needed.)   What is wrong with this predicted​ value? Choose the correct answer below.   A. It is…

Show the best fitted line on scatter diagram and Find the predicted value for each y using the exposure time and the equation obtained in part b (b. Find the equation of regression line between radiation doses on exposure time .usingleast square method)

The data show the chest size and weight of several bears. Find the regression​ equation, letting chest size be the independent​ (x) variable. Then find the best predicted weight of a bear with a chest size of 63 inches. Is the result close to the actual weight of 562 ​pounds? Use a significance level of 0.05. Chest_size_(inches)   Weight_ (pounds)58                                  41450                                  31265                                  49959                                  45059                                  45648                                  260 What is the regression equation?^y = ____ + _____ x (round to one decimal place as needed.)What Is the best predicted weight of a bear with a chest size of 63 inches? ^y =____ pounds (round one decimal as needed)Is the result close to the actual weight of 452 pounds?(a) This result is very close to the actual weight of the bear.(b) This result is close to the actual weight of the bear.(c) This result is exactly…

The data show The chest size and weight of several bears find regression equation, letting chest size be the independent variable then find the best predicted weight of a bear with a chest size of 51 inches is the result close to the actual weight of 422 pounds use a significance level of 0.05 Chest size : 45, 50, 43, 43, 52, 52. Weight : 352, 374, 275, 314, 440, 367.

The data show the bug chirps per minute at different temperatures. Find the regression​ equation, letting the first variable be the independent​ (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted​ value?   Chirps in 1 min 924 1150 840 1166 1087 930   Temperature ​(°​F) 77.5 84.6 74.1 91 79.6 79.7 What is the regression​ equation? What is the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per​ minute? What is wrong with this predicted​ value? Choose the correct answer below. A. It is unrealistically high. The value 3000 is far outside of the range of observed values. B. The first variable should have been the dependent variable. C. It is only an approximation. An unrounded value would be considered accurate. D. Nothing is wrong with this value. It can be…

Write the linear model to test the hypothesis that there is no treatment effect. Clearly describe each term in the model, and the range of the subscripts. Write the null hypothesis that you are testing.   Call: lm(formula = score ~ list, data = hearing)   Residuals:      Min       1Q   Median       3Q      Max -14.7500  -5.5833  -0.2083   6.3333  16.4167   Coefficients:             Estimate Std. Error t value Pr(>|t|)    (Intercept)   32.750      1.612  20.315  < 2e-16 *** listList2     -3.083      2.280  -1.352  0.17955    listList3     -7.500      2.280  -3.290  0.00142 ** listList4     -7.167      2.280  -3.144  0.00225 ** --- Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1   Residual standard error: 7.898 on 92 degrees of freedom Multiple R-squared:  0.1382,  Adjusted R-squared:  0.1101 F-statistic: 4.919 on 3 and 92 DF,  p-value: 0.00325