for a fixed sample size as the number of indeoendent variables in a regression model increases...

for a fixed sample size as the number of indeoendent variables in a regression model increases the power of the regression decreases. T or F

The width of a 95% confidence interval around a relative risk increases as the sample size decreases. T or F

Expert Solution

1) True ...

R2 increases with the increase in the number of predictors used in the model, even if those variables are only weakly associated with the response. And including those predictors [which do not significantly contribute to the model for predicting the response] leads to ‘overfitting’ issue.

This is due to the fact that adding another variable to the least squares equations must allow us to fit the training data (though not necessarily the testing data) more accurately. Thus, the R2 statistic, which is also computed on the training data, must increase. Hence, in case of MRA (multiple regression analysis), it is suggested to look for improvement in the value of adjusted R2. Other measures for accuracy/fit of the model may be RSE, p-value for ANOVA (F-statistics).

2) True.....Increasing the sample size decreases the width of confidence intervals, because it decreases the standard error.

milcah answered 1 year ago

A researcher estimated the following regression model with a sample size of 36. ?? = ?0...

A researcher estimated the following regression model with a sample size of 36. ?? = ?0 + ?1??1 + ?2??2 + ? The researcher wanted to find out whether there is heteroscedasticity in the error variance and so applied the White’s heteroscedasticity test. The result is as follows: ?? = −5.8417 + 2.5629??1 + 0.6918??2 − 0.4081??1 2 − 0.0491??2 2 + 0.0015??1??2 R 2 = 0.2143 What conclusion can you assist the researcher to draw at 5 percent and...

1. Consider the linear regression model for a random sample of size n: yi = β0...

1. Consider the linear regression model for a random sample of size n: yi = β0 + vi ； i = 1, . . . , n, where v is a random error term. Notice that this model is equivalent to the one seen in the classroom, but without the slope β1. (a) State the minimization problem that leads to the estimation of β0. (b) Construct the first-order condition to compute a minimum from the above objective function and use...

1. You are given with the regression result that shows the regression model with k variables....

1. You are given with the regression result that shows the regression model with k variables. Answer the following parts: a) How do you tell that a certain variable is influential? b) Suppose the theoretical issue said there exist a linear constraint, how do you figure out the constraint holds? c) Suppose you have two sets of explanatory variables; how did you consider which set is the better one? d) What’s the meaning of R-squared? Should we always look for...

As the sample size increases the standard error becomes smalller the sampling error increases the population...

As the sample size increases the standard error becomes smalller the sampling error increases the population standard deviation increases the standard error becomes larger The purpose of the finite corretion factor for the standard error of the mean is to reflect the fact that the sampling error is higher for a finite population when compared to an infinite population sampling error is lower for a finite population when compared to an infinite population sample size is not at least 30...

What is the role of control variables in a fixed-effects model?

what variables are used for a regression model. in regards to finding out the outcome of...

what variables are used for a regression model. in regards to finding out the outcome of a loan application at a financial institution.

1. A multiple linear regression model should not be used if: A The variables are all...

1. A multiple linear regression model should not be used if: A The variables are all statistically significant. B The coefficient of determination R2 is large. C Both of the above. D Neither of the above. 2. Consider a multiple linear regression model where the output variable is a company's revenue for different months, and the purpose is to investigate how the revenue depends upon the company's advertising budget. The input variables can be time-lagged so that the first input...

The regression equation is Ŷ = 30 + 2.56X, the sample size is 14, and the...

The regression equation is Ŷ = 30 + 2.56X, the sample size is 14, and the standard error of the slope is 0.97. What is the critical value to test the significance of the slope at the 0.05 significance level? Multiple Choice z = ±1.96 t = ±2.179 t = ±2.145 t = +2.145

As the sample size INCREASES for computing a confidence interval, the width of the confidence interval...

As the sample size INCREASES for computing a confidence interval, the width of the confidence interval DECREASES. 12 When the population standard deviation sigma is assumed known, a confidence interval can assume NORMALITY of the SAMPLE MEAN if the sample size is greater than 30. 12 A SYMMETRIC histogram implies the plotted variable is NORMALLY distributed. 12 The goal when using confidence intervals is to have WIDE INTERVALS to be assured that the interval contains the population parameter. 12 A...

Develop an estimated regression equation with annual income and household size as the independent variables. Discuss...

Develop an estimated regression equation with annual income and household size as the independent variables. Discuss your findings - Income ($1000s) Household Size Amount Charged ($) 54 3 4,016 30 2 3,159 32 4 5,100 50 5 4,742 31 2 1,864 55 2 4,070 37 1 2,731 40 2 3,348 66 4 4,764 51 3 4,110 25 3 4,208 48 4 4,219 27 1 2,477 33 2 2,514 65 3 4,214 63 4 4,965 42 6 4,412 21 2 2,448...

Question