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- I need solutions for d) and e). Please.Solve the second question in regression analysis12.6 SCUBA divers have maximum dive times they cannot exceed when going to different depths. The datain Table 12.4 show different depths with the maximum dive times in minutes. Use your calculator to find the leastsquares regression line and predict the maximum dive time for 110 feet.X (depth in feet) Y (maximum dive time)50 8060 5570 4580 3590 25100 22Table 12.4The third exam score, x, is the independent variable and the final exam score, y, is the dependent variable. We will plot aregression line that best "fits" the data. If each of you were to fit a line "by eye," you would draw different lines. We can usewhat is called a least-squares regression line to obtain the best fit line.Consider the following diagram. Each point of data is of the the form (x, y) and each point ofthe line of best fit using leastsquares linear regression has the form (x, ŷ).The ŷ is read "y hat" and is the estimated value of y. It is the value of y obtained using the regression line. It is not generallyequal…
- he following table shows the annual number of PhD graduates in a country in various fields. NaturalSciences Engineering SocialSciences Education 1990 70 10 60 30 1995 130 40 100 50 2000 330 130 280 140 2005 490 370 460 210 2010 590 550 830 520 2012 690 590 1,000 900 (a)With x = the number of social science doctorates and y = the number of education doctorates, use technology to obtain the regression equation. (Round coefficients to three significant digits.) y(x) = Use technology to obtain the coefficient of correlation r. (Round your answer to three decimal places.) r =ANSWER THE FOLLOWING QUESTION.Bxi + €i, where €; are independently and Consider a simple linear regression model Y; = identically distributed with mean 0 and variance o?, and i = 1,..., n. Note: this model does not have a intercept term. Derive the Best Linear Unbiased Estimator (BLUE) for B. Denote this by BBLUE. Make sure to state why this is the BLUE.
- There may be an association between a country's birthrate and the life expectancy of its inhabitants. A report this past year, coming from a random sample of 20 countries, contained the following information: the least-squares regression equation relating the two variables number of births per one thousand people (denoted by x) and female life expectancy (denoted by y and measured in years) is y = 82.28 – 0.51 x, and the standard error of the slope of this least-squares regression line is approximately 0.35. Based on this information, test for a significant linear relationship between these two variables by doing a hypothesis test regarding the population slope B,. (Assume that the variable y follows a normal distribution for each value of x and that the other regression assumptions are satisfied.) Use the 0.10 level of significance, and perform a two-tailed test. Then complete the parts below. (If necessary, consult a list of formulas.) (a) State the null hypothesis H, and the…ruan Use wage1.txt data set for this question. Consider the following regression: logtwage)-Bo-Beduc-3.exper+u. Suppose we want to test whether the return of an additional year in school will pay more than spending an additional year in the labor market Which of the following is the correct set of hypotheses for this test? Ho: 1-2 HA: 1-20 31 Ho: 1-2 HA: 1-8 270 Ho: 1-220HA: 1-³ 20 Ho: 1-2 HA: 1-820 0.91Suppose x1 ans x2 are predictor variables for a response variable y. a. The distribution of all possible values of the response variable corresponding to particular values of the two predictor variables is called a distribution of the response variable. b. State the four assumptions for multiple linear regression inferences.
- Show calculations or explanation for each question. a) Which of the following techniques is used to predict the value of one variable on thebasis of other variables?a. Correlation analysisb. Coefficient of correlationc. Covarianced. Regression analysis b) In the least squares regression line, y^=3-2x the predicted value of y equals:a. 1.0 when x = −1.0b. 2.0 when x = 1.0c. 2.0 when x = −1.0d. 1.0 when x = 1.0 c) In the simple linear regression model, the y-intercept represents the:a. change in y per unit change in x.b. change in x per unit change in y.c. value of y when x = 0.d. value of x when y = 0.2. This question is about logistic regression. The outcome variable is success (1=success, 0=failure), and we have two groups of observations: group A and group B. a. Assume that on average, the odds of success is x for group A members. What is the average probability of success (p) for group A? Please write down p as a function of x. Given an x, is there a unique p? b. Assume that on average, the odds ratio for success of group A over group B is 2. The average probability of success for group A is pA and that the average probability of success for group B is pg. Is the set of Paand pg unique? c. The logistic regression of success ~ group (link=logit) returns a coefficient estimate of -1.3863 for the dummy variable group (1=group A, 0=group B). Interpret this coefficient estimate.Use the following linear regression equation to answer the questions. x1 = 2.0 + 3.6x2 – 7.8x3 + 2.1x4 a) Suppose x3 and x4 were held at fixed but arbitrary values and x2 increased by 1 unit. What would be the corresponding change in x1?b) Suppose x2 increased by 2 units. What would be the expected change in x1?c) Suppose x2 decreased by 4 units. What would be the expected change in x1?
