Q:

yx1x2

161529

463748

342428

263222

494728

111342

414333

131226

475848

161944

Consider the data on the table, where y is the dependent (or output) variable and x1 and x2 are potential explanatory (or input) variables.

1. Perform a regression analysis using y as the output and x1 as the only input variable.

1.1 Is the regression meaningful?

a) Yes, because the multiple and adjusted R square are both quite high, which is good.

b) Yes, because the pvalue associated to the F statistic is quite small.

c) No, because the difference between the adjusted and multiple R square is too large.

d)No, because the pvalue associated to the coefficient of x1 is too small.

1.2 Is it reasonable to assume that the intercept is zero?

a) Yes, because the estimated coefficient is itself close to zero.

b) No, because the pvalue associated to the intercept is far from zero.

c)No, because the pvalue associated to the intercept is close to zero.

d) Yes, because the pvalue associated to the intercept is quite high according to the standards.

1.3 Based on your results, which one of the following is true?

a) 92% of the variability in y is explained by x1.

b)According to the F statistic, there's evidence that the intercept is zero.

c)According to a 95% CI, there's evidence to think that the intercept is not zero.

d)According to its pvalue, we should reject the hypothesis that the coefficient of x1 is zero.

1.4 According to the estimated regression equation, the predicted value for y when x1=30.5 is

a) 30.3

b) 107.7

c)-23.3

d)It doesn't exist, since that value is not reported in the data

2. Perform a regression analysis using y as the output variable and x1 and x2 as predictor variables

2.1 Is the regression with two predictors meaningful now?

a)Yes, because the multiple R remain the same

b)Yes, according to the F statistic and its pvalue

c)No, since the adjusted R squared diminished

d) No, since the standard error increased around 6.5%

2.2 Is there evidence to think that the intercep is zero?

a) No, since the estimated coefficient (intercept) is celarly very different from zero

b)Yes, since the estimated coefficient (intercept) is quite small and close to zero.

c)No, since the estimated coefficient (intercept) has a small pvalue

d)Yes, since the estimated coefficient (intercept) has a relatively large pvalue

2.3 Conduct a test based on the extra sum of squares to decide if adding x2 is significant in the model

2.3.1 The value of the test statistic is

a)0.045

b)-0.051

c)0.002

d)-0.002

2.3.2 The critical value for the test (at the 0.07 significance) is

a)4.56

b)7.37

c)0.01

d)6.03

2.3.3 According to the previous two answers, we can conclude that

a)Adding x2 to the model helps to better explain y

b)Adding x2 to the model is not significant

c)It's not convenient to eliminate x2 from the model

d)It's better to keep x2 instead of x1 in the model

2.4 According to the estimated regression equation, the prediction for y when x1=30.5 and x2=23 is

a)30.9

b)23.9

c)25.9

d)Since both values are not in the data set, it's not possible to determine that