Question

Need help with stats true or false questions

Decide (with short explanations) whether the following statements are true or false a) We consider the model y-Ao +A(z) +E. Let (-0.01, 1.5) be a 95% confidence interval for A In this case, a t-test with significance level 1% rejects the null hypothesis Ho : A-0 against a two sided alternative. b) Complicated models with a lot of parameters are better for prediction then simple models with just a few parameters c) The following formulas in R specify all the same model: fit-lm(z-x*y) fit-lm(z-(xty)-2) d) It can happen that all individual t-tests in a Regression do not reject the null hypothesis, although the global F-test is significant e) In a simple linear regression model with explanatory variable x and outcome variable y, we have these summary statistics x-10, sz = 3 Sy-5 and у-20. For a new data point with x = 13, it is possible that the predicted value is y = 26. f) A standard multiple regression model with continuous predictors rı and r2, a categorical predictor T with four values, an interaction between r1 and T, and an intercept has for its model coefficients an 11 x 1 vector β g) In a standard multiple regression model, if a plot of residuals versus fitted values shows a fan-shaped pattern with residuals becoming more spread out as fitted values increase, a log transformation of the response variable may result in data more consistent with model assumptions h) If the outcome variable is continuous and all explanatory variables take values 0 or 1, a logistic regression model is most appropriate i) Suppose we fit two regression models with the same y and explanator variables, but one model uses robust standard errors and the other model uses non-robust standard errors. The estimated coefficients for the predictors in the two models will be identical. j) After fitting a multiple regression model, a histogram of the residuals helps you detect if the linearity assumption of the model is violated k) In OLS regression, the residuals are assumed to follow a standard normal distribution. 1) Leverage points should always be removed from the regression analysis m) One squareroot-transformed the response variable and now wants to calculate confidence intervals on the original scale. He/she therefore just needs to square the confidence intervals on the transformed scale. n) There are two predictors in a multiple linear regression which are not significant. The global F-test is highly significant. For this reason, it is better not to remove both predictors simultaneously depend variable, or both, does not change the regression R2 the same or fall must fail to reject it at a significance level of α-0.10 o) The process of multiplying the dependent variable by a constant, adding a constant to the p) If an extra explanatory variable is added to a regression, the estimator of σ (se) will remain q) If we fail to reject the null hypothesis (Ho) at a significance level of α 0.05, then we also r) The error term in logistic regression has a binomial distribution. s) The standard linear regression model (under the assumption of normality) is not appropriate t) Backward and forward stepwise regression will generally provide different sets of selected u) BIC penalizes for complexity of the model more than AIC. for modeling binomial response data. variables when p, the number of predicting variables, is large

Answer 1

(a)

False, Because 95% confidence interval [-0.01, 1.5]

The confidence interval include zero in it hence do not reject H0: B1 = 0.

(b)

False. The prediction of model is based. significance of coeffient and model.

(c)

False. The three models are different.

z ~ x + y + x : y

z ~ x * y

z ~ (x + y)^2

All three are different.

(d)

True, it needs to be true see sometimes global F - test is significant but individual. Coefficient is non-significant (means do not).

Reject H0.

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