Dummy Variable Refer to Data Set 18 “Bear Measurements” in App...

Question

Dummy Variable Refer to Data Set 18 “Bear Measurements” in Appendix B and use the sex, age, and weight of the bears. For sex, let 0 represent female and let 1 represent male. Letting the response variable represent weight, use the variable of age and the dummy variable of sex to find the multiple regression equation. Use the equation to find the predicted weight of a bear with the characteristics given below. Does sex appear to have much of an effect on the weight of a bear?

Female bear that is 20 years of age
Male bear that is 20 years of age

Female bear that is 20 years of age

Male bear that is 20 years of age

Accepted Answer

Hello, everyone. Let's take a look at this question together. Refer to the data set employee salary analysis given below. The data set includes employee gender, years of experience, and annual salary. For gender, lets 0 represent female and 1 represent male. So here we have our data set, and we have to determine, using the salary as a response variable, determine the multiple regression equation using variable experience and the dummy variable for gender, then use the equation to predict salary for an employee with the characteristics given below, which are a female employee with 10 years of experience and a. Male employee with 10 years of experience, as well as we have to determine does gender appear to have a significant effect on salary. So in order to solve this problem, we must first assume a multiple linear regression model with the formula Y equals B0 plus B1 multiplied by X1 plus B2 multiplied by X2, where X1. To the years of experience, X2 refers to the gender. Y is the salary, and B, B1, and B2 are the regression coefficients, which the regression coefficients can be calculated by using ATI 84 + calculator through the following steps, where we enter the data into the calculator and then perform multiple. Regressions, and the values that the calculator provides are the intercept or B zero is approximately 29.17. The experience coefficient or B1 is approximately 4.17, and the gender coefficient or B2 is approximately 3.33. So using those values and our multiple linear regression model. The regression equation is Y equals 29.17 plus 4.17 X1 plus 3.33 X2. So then we use the equation to predict the salary for the two different employees. First, for the female employee with 10 years of experience, where X1 is equal to 10 and X2 is equal. To 0, we plug in the values into our regression equation, and the salary Y is equal to 29.17 plus 4.17 multiplied by 10, plus 3.33 multiplied by 0, which equals 70.87. So the salary of the female employee with 10 years of experience is 70.87. And then we calculate the same for the male employee with 10 years of experience, where X1 is equal to 10, and X2 is equal to 1, giving us the salary Y, which is equal to 29.17, plus 4.17 multiplied by 10, plus 3.33 multiplied by 1, giving us 74. 2, which 74.2% is the salary for the male employee with 10 years of experience. So from the data that we have calculated, we can identify that the coefficient for gender B2, which is approximately 3.33, suggests that the male employees earn $3300 more than The female employees with the same experience, which indicates a noticeable impact on salary based on gender. And so looking back at our answer choices, we can identify that the answer choice containing the correct multiple regression equation and whether gender appears to have a significant effect on salary is answer choice A. As the multiple regression equation is in fact Y equals 29.17 plus 4.17 X1 plus 3.33 X2, and we found out that gender does have a significant effect on salary. As the male employees earned $3300 more than the female employees with the same experience. So answer choice A is the correct answer, and all other answer choices are incorrect. I hope you found this video to be helpful. Thank you and goodbye.

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Key Concepts

Dummy Variables

Multiple Regression

Interpreting Regression Coefficients

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