Suppose we are interested in the effect of gender on incomeand we estimate a model in which income is the dependentvariable and the regressor is a dummy variable that takes thevalue 1 if the person is a man and O if the person is a woman.If we instead estimate a model that includes a dummy variablefor women (takes value 1 if woman and 0 if man), thenThe fit of the model will change.We will get a different conclusion for testing a null hypothesis thatthere is no gender effect.The coefficient on the dummy variables will differ across models,but the estimated difference of mean income between men andwomen will not change.The coefficient on the dummy variables will be exactly the same.

It is required to identify the correct statement regarding a dummy variable in regression analysis.

Answered: Suppose we are interested in the effect…

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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Suppose when you add flexibility to your model by adding higher-order terms or more predictor variables that you begin to see the test or validation error (MSE or SSE evaluated on the test or validation set) begin to increase away from the training error. What kind of a problem are your models experiencing?
A recent Gallup survey of a random sample of Americans (18 and older) found that the average number of alcoholic drinks consumed per week (drinks) by males was 4.2 and by females was 1.4.[¹] Suppose we use the underlying survey data to estimate a least-squares regression of the average number of drinks a person reports consuming per week (Drinks;) on a dummy variable equal to 1 if i is female and 0 otherwise (Female;). (Assume all respondents identify as either male or female.) The estimated regression line equation can be written as: Drinks = a +bFemale Alcohol Consumption by Gender What is the numerical value of b?
The null hypothesis being tested in the least-squares regression output for B is B1 = B1,0=1. True False
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…
A financial analyst is examining the relationship between stock prices and earnings per share. She chooses fifteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least- squares regression line to be y = -0.137 +0.043x. This line, along with a scatter plot of her data, is shown below. Earnings per share, x (in dollars) Current stock price, y (in dollars) 59.10 2.35 30.89 1.34 40.95 1.76 29.50 1.02 48.19 1.63 37.29 1.68 21.65 0.63 15.95 0.63 1- 26.45 1.02 0.5 32.26 1.53 17.72 0.78 42.86 1.50 Earnings per share (in dollars) 36.45 1.17 57.56 2.84 40.32 1.06 Current stock price (in dollars)
A financial analyst is examining the relationship between stock prices and earnings per share. She chooses sixteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with X denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least- squares regression line to be ŷ=-0.231+0.045x. This line, along with a scatter plot of her data, is shown below. Earnings per share, x Current stock price, y (in dollars) (in dollars) 58.47 2.17 30.64 1.44 41.03 1.45 41.26 1.05 26.04 0.80 42.80 1.84 18.10 0.77 21.73 0.62 29.68 0.74 32.97 1.64 37.74 1.56 57.98 2.70 38.05 1.16 49.40 1.59 15.49 0.59 51.67 2.65 Send data to calculator ✓ Send data to Excel Current stock price (in dollars) Based on the analyst's data and regression line, complete the following. 05 0 10 30 x x x **…
Suppose we have a multiple regression model with 2 predictors and an intercept. (Without any interaction or higher order terms, we have only the 2 predictors in the model and the intercept.) We have only n= 6 observations (so it would be rather silly to fit this model to this data, but let's pretend it is reasonable). We find the values of the first 5 residuals are: 2.6, 2.3, 2.5, -1.5, -1.4 What is the value of MSRes for this multiple regression model?
Suppose John is a high school statistics teacher who believes that watching many hours of TV leads to lower test scores. Immediately after giving the most recent test, he surveyed each of the 24 students in his class and asked them how many hours of TV they watched that week. He then matched each student's test grade with his or her survey response. After compiling the data, he used hours of TV watched to predict each student's test score. He found the least-squares regression line to be ?̂ =−1.5?+85y^=−1.5x+85. He also calculated that the value of ?r, the correlation coefficient, was −0.61. Which of the choices identifies the correct value of the coefficient of determination, ?2R2, and gives a correct interpretation of its meaning?
A financial analyst is examining the relationship between stock prices and earnings per share. She chooses sixteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least- squares regression line to be y =-0.303 +0.048x. This line, along with a scatter plot of her data, is shown below. Earnings per share, x (in dollars) Current stock price, y (in dollars) 36.37 1.61 52.57 2.80 57.34 2.81 36.26 1.29 57.82 2.24 41.36 1.66 51.02 1.71 Xx X 31.83 0.78 27.38 0.82 14.63 0.51 it 0.5. 33.70 + + 1.64 39.97 1.06 42.39 1.91 Earnings per share (in dollars) 18.83 0.68 21.10 0.83 29.79 1.33 Send data to calculator Send data to Excel Based on the analyst's data and regression line, answer the following. (a)…
A financial analyst is examining the relationship between stock prices and earnings per share. She chooses sixteen publicly traded companies at random and records for each the company's current stock price and the company's earnings per share reported for the past 12 months. Her data are given below, with x denoting the earnings per share from the previous year, and y denoting the current stock price (both in dollars). Based on these data, she computes the least-squares regression line to be y = -0.224+0.044x. This line, along with a scatter plot of her data, is shown below. Earnings per share, x (in dollars) 30.13 42.76 58.46 37.50 57.30 27.60 30.17 41.82 50.09 38.18 22.41 33.44 39.66 14.13 17.85 53.57 Send data to calculator V Current stock price, y (in dollars) 1.41 1.37 2.25 1.54 2.64 0.90 0.79 1.04 1.56 1.15 0.65 1.72 1.80 0.51 0.71 2.74 Send data to Excel Current stock price (in dollars) Based on the analyst's data and regression line, complete the following. 2.5- 2+ 1.5. 0.5- 0…

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