new answers

hw2/answers

@@ -1,61 +1,86 @@
 
 
-1. Describe the null hypotheses to which the p-values given in Table 3.4
-correspond. Explain what conclusions you can draw based on these
-p-values. Your explanation should be phrased in terms of sales , TV ,
-radio , and newspaper , rather than in terms of the coefficients of the
-linear model.
+1. Describe the null hypotheses to which the p-values given in Table
+   3.4 correspond. Explain what conclusions you can draw based on
+   these p-values. Your explanation should be phrased in terms of
+   sales , TV , radio , and newspaper , rather than in terms of the
+   coefficients of the linear model.
+
+
+	P-values that are very small indicate that the model for that
+	predictor is likely to account for a significant amount of the
+	association between the predictor and the response. If that is
+	true, then, we reject the null hypothesis, and conclude that a
+	relationship exists between the predictor and the response. The
+	p-values computed from the response of sales to marketing budget
+	for each marketing paradigm indicate will give us insight into
+	which of these predictors have a strong relationship with sales
+	of this product.
+
+	TV marketing and radio marketing both have a strong relationship
+	to sales, according to their linear regression p-values, but
+	newspaper advertising does not appear to be effective, given
+	that the linear model does not account for much of the variation
+	in sales across that domain. We can conclude that cutting back
+	on newspaper advertising will likely have little effect on the
+	sales of the product, and that increasing TV and radio
+	advertising budgets likely will have an effect. Furthermore, we
+	can see that radio advertising spending has a stronger
+	relationship with sales, as the best-fit slope is significantly
+	more positive than the best fit for TV advertising spending, so
+	increasing the radio advertising budget will likely be more
+	effective.
 
 
 
-
-3. Suppose we have a data set with five predictors, X 1 = GPA, X 2 = IQ,
-X 3 = Gender (1 for Female and 0 for Male), X 4 = Interaction between
-GPA and IQ, and X 5 = Interaction between GPA and Gender. The
-response is starting salary after graduation (in thousands of dollars).
-Suppose we use least squares to fit the model, and get β₀ = 50, β₁ =
-20, β₂ = 0.07, β₃ = 35, β₄ = 0.01, β₅ = −10.
+3. Suppose we have a data set with five predictors, X₁ = GPA, X₂ =
+   IQ, X₃ = Gender (1 for Female and 0 for Male), X₄ = Interaction
+   between GPA and IQ, and X₅ = Interaction between GPA and Gender.
+   The response is starting salary after graduation (in thousands of
+   dollars). Suppose we use least squares to fit the model, and get
+   β₀ = 50, β₁ = 20, β₂ = 0.07, β₃ = 35, β₄ = 0.01, β₅ = −10.
 
 	(a) Which answer is correct, and why?
-		i. For a fixed value of IQ and GPA, males earn more on average
-		than females.
+		i. For a fixed value of IQ and GPA, males earn more on
+		   average than females.
 
 		ii. For a fixed value of IQ and GPA, females earn more on
 		average than males.
 
-		iii. For a fixed value of IQ and GPA, males earn more on average
-		than females provided that the GPA is high enough.
+		iii. For a fixed value of IQ and GPA, males earn more on
+		average than females provided that the GPA is high enough.
 
 		iv. For a fixed value of IQ and GPA, females earn more on
 		average than males provided that the GPA is high enough.
 
-	(b) Predict the salary of a female with IQ of 110 and a GPA of 4.0.
+	(b) Predict the salary of a female with IQ of 110 and a GPA of
+	4.0.
 
-	(c) True or false: Since the coefficient for the GPA/IQ interaction
-	term is very small, there is very little evidence of an interaction
-	effect. Justify your answer.
+	(c) True or false: Since the coefficient for the GPA/IQ
+	interaction term is very small, there is very little evidence of
+	an interaction effect. Justify your answer.
 
 
 
 
-4. I collect a set of data (n = 100 observations) containing a single
-predictor and a quantitative response. I then fit a linear regression
-model to the data, as well as a separate cubic regression, i.e. Y =
-β₀ + β₁ X + β₂ X² + β₃ X³ + .
+4. I collect a set of data (n = 100 observations) containing a
+   single predictor and a quantitative response. I then fit a linear
+   regression model to the data, as well as a separate cubic
+   regression, i.e. Y = β₀ + β₁ X + β₂ X² + β₃ X³ + .
 
-	(a) Suppose that the true relationship between X and Y is linear,
-	i.e. Y = β₀ + β₁ X + . Consider the training residual sum of
-	squares (RSS) for the linear regression, and also the training
-	RSS for the cubic regression. Would we expect one to be lower
-	than the other, would we expect them to be the same, or is there
-	not enough information to tell? Justify your answer.
+	(a) Suppose that the true relationship between X and Y is
+	linear, i.e. Y = β₀ + β₁ X + . Consider the training residual
+	sum of squares (RSS) for the linear regression, and also the
+	training RSS for the cubic regression. Would we expect one to be
+	lower than the other, would we expect them to be the same, or is
+	there not enough information to tell? Justify your answer.
 
 	(b) Answer (a) using test rather than training RSS.
 
-	(c) Suppose that the true relationship between X and Y is not linear,
-	but we don’t know how far it is from linear. Consider the training
-	RSS for the linear regression, and also the training RSS for the
-	cubic regression. Would we expect one to be lower than the
-	other, would we expect them to be the same, or is there not
-	enough information to tell? Justify your answer.
-	(d) Answer (c) using test rather than training RSS.
+	(c) Suppose that the true relationship between X and Y is not
+	linear, but we don’t know how far it is from linear. Consider
+	the training RSS for the linear regression, and also the
+	training RSS for the cubic regression. Would we expect one to be
+	lower than the other, would we expect them to be the same, or is
+	there not enough information to tell? Justify your answer. (d)
+	Answer (c) using test rather than training RSS.