Question

1. Why is there a t-test performed in association with the
b_{1} coefficient? What does the result of the t-test tell
us?

2. b_{0} is the value of Y when what?

3. Does a flatter regression line mean a stronger or weaker
relationship between the predictor and outcome variables? Please
explain.

Answer #1

1.

We performed the t test in association with the b_{1}
coefficient because the standard deviation of the true slope
coefficient is unknown. The result of the t-test tell about the
significance of the slope coefficient in the model.

2.

b_{0} is the value of Y when all the independent
variables of the model are 0.

3.

The flatter regression line tells that the rate of change in outcome variable is very low with the increase in the predictor variable. In other words, the slope coefficient value of the regression line is low and thus, there is a weaker relationship between the predictor and outcome variables.

5. You have performed a simple linear regression model and ended
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(a) In your own words, describe clearly what the coefficient of
determination, r^2, measures.
(b) Suppose that your calculations produce r^2 = 0.215. As
discussed in textbook, what can you conclude from this value?
Furthermore, what can you say about the strength and direction of
the relationship between the predictor and the response
variable?

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1
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