Answered: What is a dependent variable?

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Math

Calculus

What is a dependent variable?

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

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The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 13 In the MLR model, what do we mean by Heteroskedasticity? That the error term depends on the values of the explanatory variables That all the explanatory variables have different variance That the variance of the error term is a function of the explanatory variables That the variance of the error term is constant QUESTION 14 Suppose that in the model Y=b0+b1*X1+u, we add a variable that is correlated with both Y and X1. What will happen…
2. You are president of the high school band booster club. You have arranged for school's jazz band to perform at a local coffee shop for three hours. In exchance the performance, the booster club will receive three-quarters of the shop's gross receint during that three-hour period. a. Let r be the independent variable representing the gross receipts of the coffee shon during the performance. Let y be the dependent variable representing the share of the gross receipts that the coffee shop will donate to the band boosters. Write an equation relating r and y. b. Use the equation from part a to complete the following table. x, TOTAL GROSS RECEIPTS ($) 250 500 750 1000 y, BOOSTERS' SHARE ($) c. If the coffee shop presents you with a check for $650, what were the gross recepo during the performance? Estimate your answer using a numerical approach.
An engineer wants to determine how the weight of a gas-powered car, x, affects gas mileage, y. The accompanying data represent the weights of various domestic cars and their miles per gallon in the city for the most recent model year. Complete parts (a) through (d) below. (a) Find the least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable. y=nothingx+(nothing) (Round the x coefficient to five decimal places as needed. Round the constant to one decimal place as needed.) (b) Interpret the slope and y-intercept, if appropriate. Choose the correct answer below and fill in any answer boxes in your choice. (Use the answer from part a to find this answer.) A. A weightless car will get nothing miles per gallon, on average. It is not appropriate to interpret the slope. B. For every pound added to the weight of the car, gas mileage in the city will decrease by nothing mile(s) per gallon, on…
The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 4 Suppose we have an SLR model, where the dependent variable (Y) represents ‘how satisfied someone is with his/her life, from 0 to 100’ (the higher the value, the higher the satisfaction with life), and the explanatory variable (X1) represents ‘personal annual income in £1,000’. The estimated OLS regression line is: Yhat = 33.2 + 0.74*X1. According to this model, what is the predicted life satisfaction, for someone with…
The following regression model investigates the determinants of years of schooling. educ = Bo + B₁ * motheduc + B₂ fatheduc + ß* income +84 * ability + u where motheduc is mother's education, fatheduc is father's education, sibs is number of siblings, and ability is a person's ability. Write the reparameterized model and explain how you would use it to test the hypothesis that mother's education and father's education have the same effect on years of schooling.
A statistical program is recommended. An automobile dealer conducted test to determine whether the time needed to complete a minor engine tune-up depends on whether a computerized engine analyzer or an electronic analyzer is used. Because tune-up time varies among compact, intermediate, and full-sized cars, the three types of cars were used as blocks in the experiment. The data (time in minutes) obtained follow. x₂ Analyzer 0 Computerized Electronic Define all variables. Let x₁ = 0 if a computerized analyzer is used, or let x₁ = X3 O Ho: B₁ * 0 H₂: B₁ = 0 0 Compact 1 52 Car 41 Compact Intermediate Full Size Intermediate O Ho: One or more of the parameters is not equal to zero. H₁: B₂ =B3 = 0 Car 57 Find the p-value. (Round your answer to three decimal places.) p-value = 43 Use α = 0.05 to test for any significant differences between the two analyzers. State the null and alternative hypotheses. O Ho: B₁ = 0 H₂: B₁ = 0 Full Size o Ho: Ba = By = 0 H₂: One or more of the parameters is not…
The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 28 Suppose your estimated MLR model is: Y_hat = -30 + 2*X1 + 10*X2 Suppose the standard error for the estimated coefficient associated with X2 is equal to 5. Now, suppose that for some reason we multiply X2 by 5 and we re-estimate the model using the rescaled explanatory variable. What will be the value of the estimated coefficient of X2 and its standard error? The estimated coefficient of X2 will be equal to 50 and its standard error will be…
1.)fill in the blanks. Based on the physician's study, the predictor variable, X is_____and the response variable, Y, is________. 2.) As described in the article, the relation between age and peak heart is a______. - positive relation - negative relation - no relation 3.) Provide the regression line, ŷ=a+bx. Show steps/equations used to get answer. 4.) Suppose a 40 year old person is randomely selected. Use your Model to predict their peak heart rate. 5.) Based on your model, as a person ages one year, how much would you expect peak heart rate to change?
Two variables are said to interact when----? the effect of one independent variable depends on the level of the second independent variable both variables produce a change in the subjects score the two variables are differentially affected by a third variable both variable are equally influenced by a third variable
The Simple Linear Regression model is Y = b0 + b1*X1 + u and the Multiple Linear Regression model with k variables is: Y = b0 + b1*X1 + b2*X2 + ... + bk*Xk + u Y is the dependent variable, the X1, X2, ..., Xk are the explanatory variables, b0 is the intercept, b1, b2, ..., bk are the slope coefficients, and u is the error term, Yhat represents the OLS fitted values, uhat represent the OLS residuals, b0_hat represents the OLS estimated intercept, and b1_hat, b2_hat,..., bk_hat, represent the OLS estimated slope coefficients. QUESTION 16 In a t-test, suppose a researcher sets the significance level at 0.5%. What does this mean? The probability that the null hypothesis is true is 0.5% The researcher would be rejecting the null hypothesis, only if the p-value is less than 0.5% The researcher would be rejecting the null hypothesis, if the t-statistic is higher than 0.5 It does not mean anything, because the significance level can only be set at 5% QUESTION 17 In an MLR…
Psychologist wants to determine if there is a linear relationship between the number of hours a person goes without sleep and the number of mistakes he/she makes on a simple test. The following data is recorded. Hours without sleep 32 38 48 24 46 35 30 34 42 Number of Mistakes 6 8 13 5 7 6 5 8 12 Hours without sleep=x, Number of mistakes=y (a) When you test the claim at the α = 0.01, that a linear relation exists between the two variables, find the critical value. Round critical value to nearest hundredth. (e.g. 0.135 would be entered as 0.14, -0.135 would be entered as -0.14, ± 0.135 would be entered as +/-0.14). (b) Find 95% confidence interval about the slope of the true lease-square regression line. Lower , Upper . Round confidence interval to nearest thousandth. e.g. 2.3457 would be entered as 2.346 (c) Based on question (b), does any linear relation exist between hours without sleep and number of mistakes? . (Enter yes or no,…
if you score on your next statics says is converted to a z-score, which of these z-scores would you prefer?