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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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 + B121 2. E(y) = 80 +8₂2₂ 3. E(y)= Bo + Br2n+B 4. E(y) = Bo + B +B2z Option 4 Enter 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 1 Level 2 x1 X X b. What is the expected value of y corresponding to level 1 of the categorical variable? 1. E(y) = Bo + Bin 2. E(y) = Bo + B 3. E(y) = Bo + BitBa 4. E(y) = So + B121 + ₂x2 Option 2 c. What is the expected value of y corresponding to level 2 of the categorical variable? 1. E(y) = 80 + B1x1 2. E(y) = Bo + B22 3. E(3) = Bo + Biên +B 4. E(y) = Bo + Bi + B22 Option 4 d. Interpret the parameters in your regression equation. B₁ = E(yllevel 2) - E(y|level1) ✓ B2 is the change in E(y) for a 1 unit change in x2 holding the categorical variable constant.

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 + B121 2. E(y) = 80 +8₂2₂ 3. E(y)= Bo + Br2n+B 4. E(y) = Bo + B +B2z Option 4 Enter 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 1 Level 2 x1 X X b. What is the expected value of y corresponding to level 1 of the categorical variable? 1. E(y) = Bo + Bin 2. E(y) = Bo + B 3. E(y) = Bo + BitBa 4. E(y) = So + B121 + ₂x2 Option 2 c. What is the expected value of y corresponding to level 2 of the categorical variable? 1. E(y) = 80 + B1x1 2. E(y) = Bo + B22 3. E(3) = Bo + Biên +B 4. E(y) = Bo + Bi + B22 Option 4 d. Interpret the parameters in your regression equation. B₁ = E(yllevel 2) - E(y|level1) ✓ B2 is the change in E(y) for a 1 unit change in x2 holding the categorical variable constant.

Functions and Change: A Modeling Approach to College Algebra (MindTap Course List)

6th Edition

ISBN:9781337111348

Author:Bruce Crauder, Benny Evans, Alan Noell

Publisher:Bruce Crauder, Benny Evans, Alan Noell

Chapter3: Straight Lines And Linear Functions

Section3.CR: Chapter Review Exercises

Problem 15CR: Life Expectancy The following table shows the average life expectancy, in years, of a child born in...

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Life Expectancy The following table shows the average life expectancy, in years, of a child born in the given year42 Life expectancy 2005 77.6 2007 78.1 2009 78.5 2011 78.7 2013 78.8 a. Find the equation of the regression line, and explain the meaning of its slope. b. Plot the data points and the regression line. c. Explain in practical terms the meaning of the slope of the regression line. d. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 2019? e. Based on the trend of the regression line, what do you predict as the life expectancy of a child born in 1580?2300
Olympic Pole Vault The graph in Figure 7 indicates that in recent years the winning Olympic men’s pole vault height has fallen below the value predicted by the regression line in Example 2. This might have occurred because when the pole vault was a new event there was much room for improvement in vaulters’ performances, whereas now even the best training can produce only incremental advances. Let’s see whether concentrating on more recent results gives a better predictor of future records. (a) Use the data in Table 2 (page 176) to complete the table of winning pole vault heights shown in the margin. (Note that we are using x=0 to correspond to the year 1972, where this restricted data set begins.) (b) Find the regression line for the data in part ‚(a). (c) Plot the data and the regression line on the same axes. Does the regression line seem to provide a good model for the data? (d) What does the regression line predict as the winning pole vault height for the 2012 Olympics? Compare this predicted value to the actual 2012 winning height of 5.97 m, as described on page 177. Has this new regression line provided a better prediction than the line in Example 2?
We have data on Lung Capacity of persons and we wish to build a multiple linear regression model that predicts Lung Capacity based on the predictors Age and Smoking Status. Age is a numeric variable whereas Smoke is a categorical variable (0 if non-smoker, 1 if smoker). Here is the partial result from STATISTICA. b* Std.Err. of b* Std.Err. N=725 of b Intercept Age Smoke 0.835543 -0.075120 1.085725 0.555396 0.182989 0.014378 0.021631 0.021631 -0.648588 0.186761 Which of the following statements is absolutely false? A. The expected lung capacity of a smoker is expected to be 0.648588 lower than that of a non-smoker. B. The predictor variables Age and Smoker both contribute significantly to the model. C. For every one year that a person gets older, the lung capacity is expected to increase by 0.555396 units, holding smoker status constant. D. For every one unit increase in smoker status, lung capacity is expected to decrease by 0.648588 units, holding age constant.
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According to an article, one may be able to predict an individual's level of support for ecology based on demographic and ideological characteristics. The multiple regression model proposed by the authors was the following. y = 3.60-.01.x₁ +.01.x2-.07x3+.12x4+.02xs-.04x6-.01x7.04x8-.02xg+e The variables are defined as follows. y = ecology score (higher values indicate a greater concern for ecology) x₁ = age times 10 x₂ = income (in thousands of dollars) x3 = gender (1 = male, 0 = female) X4 = race (1 = white, 0 = nonwhite) X5 = education (in years) x6 = ideology (4 = conservative, 3 = right of center, 2 = middle of the road, 1 = left of center, and 0 = liberal) X7 = social class (4 = upper, 3 = upper middle, 2 = middle, 1 = lower middle, 0 = lower) x8 = postmaterialist (1 if postmaterialist, 0 otherwise) x9 = materialist (1 if materialist, O otherwise) (a) Suppose you knew a person with the following characteristics: a 30 year old, white female with a college degree (20 years of…