Problem 1 (13 points. one point each. This section consists of some true/false q

Question

Problem 1 (13 points. one point each. This section consists of some true/false questions regarding concepts of statistical inference. Indicate if a statement is true or false. (1) To conduct a valid regression analysis, both x and y must be approximately normally distributed (2) Rejecting the null hypothesis of no linear regression implies that changes in x cause changes in y (3) In linear regression we may extrapolate without danger. 4) The x values must be randomly selected in order to use a regression analysis (5) The term 1r serves as the point estimate for estimating both the mean and individual prediction ofy for a given x (6) Useful prediction intervals for y can be obtained from a regression analysis. (7) All data points will fit the regression line exactly if the sample correlation is either +1 or (8) The prediction interval for y is widest whenx is at its mean. (9) The standard error of the estimated slope of a regression model becomes larger as the dispersion (variance) ofx increases (10) When there is no linear relationship between two variables, a horizontal regression line best describes the relationship (1) Ifr> 0, then as x increases, y tends to increase (12) f a regression line is computed for data where x ranges from 0 to 30, you may safely predict y for x- 40. (13) The correlation coefficient can be used to detect any relationship between two variables

Explanation / Answer

1) True

The regression has five key assumptions:

2) False

3) False

"Extrapolation" beyond the "scope of the model" occurs when one uses an estimated regressionequation to estimate a mean µY or to predict a new response ... The moral of the story is that the trend in the data as summarized by the estimated regression equation does not necessarily hold outside the scope of the model.

4) True

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