Consider a regression study involving a dependent variable y, a quantitative independent variable 2, and a categorical independent variable with two levels (level 1 and level 2).a. Write a multiple regression equation relating 2 and the categorical variable to y.1. E(y) Bo + B1x12. E(y) = Bo + Baz3. E(y) Bo + B1x1 + B₂4. E(y) = Bo + B1n+B22Option 4Enter the values of dummy variable ₁ that are used to indicate the two levels of the qualitative variable. If your answer is zero, enter "0".Level 1Level 2x1b. What is the expected value of y corresponding to level 1 of the categorical variable?1. E(y)= Bo + Bui2. E(y)= Bo + B223. E(y) = Bo + B +4. E(3) = Bo + Bun+B22Option 2c. What is the expected value of y corresponding to level 2 of the categorical variable?1. E(y)= Bo + Bun2. E(y) = Bo + B223. E(y) = Bo + B+B4. E(y) Bo + B₁ + B₂x2Option 4d. Interpret the parameters in your regression equation.B₁ = E(y|level2) - E(y|level1)B₂ is the change in E(y) for a 1 unit change in [x2✔ holding the categorical variable constant.

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Answered: Consider a regression study involving a…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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I’m interested in seeing whether or not there is a relationship between the number of hours someone sleeps and traffic accidents. I gather data from the Department of Transportation and get the following data: X (hours of sleep) Y (Traffic accidents) 5 2 5 1 3 4 4 4 2 6 6 3 8 1 9 1 5 0 6 4 Using the above data, create a linear regression equation to predict traffic accidents from hours of sleep. What is the Pearson correlation coefficient? Is it strong or weak? Positive or negative? What is the linear regression equation? (in the form of Y’ = bX + a) How many traffic accidents might we predict with someone that gets 0 hours of sleep? How many traffic accidents might we predict with someone that gets 11 hours of sleep?
Consider a regression study involving a dependent variable y, a quantitative independent variable x1, and a categorical independent variable with three possible levels (level 1, level 2, and level 3). a. How many dummy variables are required to represent the categorical variable? b. Consider the following regression equation relating x 1 and the categorical variable to y. E(v) = Bo + B1x 1 + B 2 x 2 + B 3 x 3 1X1 + Enter the values of dummy variables x 2 and x 3 that are used to indicate the three levels of the qualitative variable. Level X 2 X 3 Select v Select v 2 Select v Select v Select v Select v c. Interpret the parameters in your regression equation. B1 is the change in E(y) to a 1 unit change in Select v holding the categorical variable constant. B2 = Select B 3 = Select
A researcher conducted a number of descriptive statistics for two variables X and Y. They were as follows: SP = 15; SSx = 3; My = 7; Mx = 3 What is b equal to (Please include the sign: e.g., -20)? What is a equal to (please include the sign: e.g., +4.0)? Using b and a construct a regression equation, and then using the regression equation, calculate the value of predicted Y when X = 2?
ANSWER THE FOLLOWING QUESTION.
1. Consider the following regression model: Fram Risk Score; = Bo + B1 × Health Insurance; + u¿ The Framingham Risk Score predicts 10-year risk of cardiovascular disease based on age, cholesterol levels, blood pressure, blood sugar, use of medication for high blood pressure, and smoking. A higher score means worse overall cardiovascular health. A researcher who collects data and regresses the Fram Risk Score against Health Insurance (= 1 if have insurance) finds that B, 2. Consider the following regression model: Class Average; = Bo + B1 x Office Hours; + u; Class Average is the students' average grade in the class at the end of the term and Office Hours is the number of office hours held by the instructor over the entire term. A researcher who collects data and regresses Class Average against Office Hours finds that, surprisingly, B V A V A
A study examined the eating habits of 20 children at a nursery school. The variables measured for each child included: calories (the number of calories eaten at lunch), time (the time in minutes spent eating lunch), and sex (male=1, female=0). A multiple linear regression model using Y = calories, X1 = time, and X2 = sex led to the following model: y=547.65-2.85x1+10.67x2 For two children who spend the same amount of time eating, one male and one female, which child is predicted to consume more calories and by how much?
1
The table below shows the number of state-registered automatic weapons and the murder rate for several Northwestern states. xx 11.7 8.1 6.7 3.3 2.7 2.3 2.2 0.3 yy 13.8 10.7 9.9 6.6 6.1 5.9 6.1 4.5 xx = thousands of automatic weaponsyy = murders per 100,000 residents Determine the regression equation in y = ax + b form and write it below. (Round to 2 decimal places) A) How many murders per 100,000 residents can be expected in a state with 6.4 thousand automatic weapons? Answer = Round to 3 decimal places. B) How many murders per 100,000 residents can be expected in a state with 6.7 thousand automatic weapons? Answer = Round to 3 decimal places.
Consider the following linear regression prediction equation: Y = 12 + -1x. What is the direction of the relationship between these two variables? a. The relationship between the observed X and the predicted Y is negative. b. The relationship between the observed X and the predicted Y is positive. c. There is no relationship between the observed X and the predicated Y. d. There is a weak relationship between the observed X and the predicted Y with no direction.
17. When the heights (in inches) and shoe lengths (also in inches) were measured for a large random sample of individuals, it was found that r = 0.89, and a regression equation was constructed in order to further explore the relationship between shoe length and height, with height being the response variable. From this information, what can we conclude? 1. The regression equation relating shoe length to height must have a positive intercept. 2. Approximately 89% of the variability in height can be explained by the regression equation. 3. Because the value of r is less than 1, we should characterize this relationship as being weak. 4. The regression equation relating shoe length to height must have a slope equal to 0.89. 5. The correlation coefficient should have no units.

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