(A) What type of pattern exists in the data?
a. Positive trend, no seasonality
b. Horizontal trend, no seasonality
c. Vertical trend, no seasonality
d. Positive tend, with seasonality
e. Horizontal trend, with seasonality
f. Vertical trend, with seasonality

(B) Use a multiple regression model with dummy variables as follows to develop an equation to account for seasonal effects in the data. Qtr1 = 1 if Quarter 1, 0 otherwise; Qtr2 = 1 if Quarter 2, 0 otherwise; Qtr3 = 1 if Quarter 3, 0 otherwise. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300) If the constant is "1" it must be entered in the box. Do not round intermediate calculation.

(C)

(D)Use a multiple regression model to develop an equation to account for trend and seasonal effects in the data. Use the dummy variables you developed in part (b) to capture seasonal effects and create a variable t such that t = 1 for Quarter 1 in Year 1, t = 2 for Quarter 2 in Year 1,… t = 12 for Quarter 4 in Year 3. If required, round your answers to three decimal places. For subtractive or negative numbers use a minus sign even if there is a + sign before the blank. (Example: -300)

(E) Compute the quarterly forecasts for next year based on the model you developed in part (d).
Do not round your interim computations and round your final answer to three decimal places.

(F) Is the model you developed in part (b) or the model you developed in part (d) more effective? If required, round your intermediate calculations and final answer to three decimal places.

id sex status income verbal gamble 1 1 51 2 8 0 2 1 28 2.5 8 0 3 1 37 2 6 0 4 1 28 7 4 7.3 5 1 65 2 8 19.6 6 1 61 3.47 6 0.1 7 1 28 5.5 7 1.45 8 1 27 6.42 5 6.6 9 1 43 2 6 1.7 10 1 18 6 7 0.1 11 1 18 3 6 0.1 12 1 43 4.75 6 5.4 13 1 30 2.2 4 1.2 14 1 28 2 6 3.6 15 1 38 3 6 2.4 16 1 38 1.5 8 3.4 17 1 28 9.5 8 0.1 18 1 18 10 5 8.4 19 1 43 4 8 12 20 0 51 3.5 9 0 21 0 62 3 8 1 22 0 47 2.5 9 1.2 23 0 43 3.5 5 0.1 24 0 27 10 4 156 25 0 71 6.5 7 38.5 26 0 38 1.5 7 2.1 27 0 51 5.44 4 14.5 28 0 38 1 6 3 29 0 51 0.6 7 0.6 30 0 62 5.5 8 9.6 31 0 18 12 2 88 32 0 30 7 7 53.2 33 0 38 15 7 90 34 0 71 2 10 3 35 0 28 1.5 1 14.1 36 0 61 4.5 8 70 37 0 71 2.5 7 38.5 38 0 28 8 6 57.2 39 0 51 10 6 6 40 0 65 1.6 6 25 41 0 48 2 9 6.9 42 0 61 15 9 69.7 43 0 75 3 8 13.3 44 0 66 3.25 9 0.6 45 0 62 4.94 6 38 46 0 71 1.5 7 14.4 10. A study of teenage gambling in Britain was performed in 2008. There is 47 observations and 5 variables. Download the data set Gambling from Blackboard and answer the following questions. a) Make a numerical and graphical summary of the data, commenting on any features that you fi interesting. Limit the output your present to a quantity that a busy reader would find sufficient. b) What percent of the variation in the response is explained by these predictors? c) Which observation has the largest (positive) residual? d) Compute the mean and median of the residuals. e) For all other predictors held constant, what would be the difference in predicted expenditure on gambling for a male compared to a female? f) Which variables are statistically significant? g) Predict the amount that a male with average status, income, and verbal score would gamble along with an appropriate 95% CI. Repeat the prediction for a male with maximal values of status, income, and verbal score. Which CI is wider and why is this result expected? h) Fit a model with just income as a predictor and use an F?test to compare it to the full model. i) Check the constant variance, normality, and linearity assumption. De- scribe your findings.

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1. Show that the lines ?/1 = y+3/ 2 = z+1/3 and x-3/2 = y/1 = z-1/-1 intersect by finding their point of intersection. Find the equation of the plane determined by these lines. Find parametric equations for the line that is perpendicular to the two lines and passes through their point of intersection.

Question 15

Rudolph has a budget of $22 to spend on rice ( R) and chicken nuggets ( N). The price of rice is $4.04 per pound, and the price of chicken nuggets is $3.28 per unit. The table below shows the marginal utilities that the consumer gets from the different quantities of both.

What is the optimal bundle of rice and chicken nuggets ( Q_R, Q_N) for Rudolph? ( Q_R, Q_N) =

Let X be a discrete random variable that takes value -2, -1, 0, 1, 2 each with probability 1/5.

Let Y=X²

a) Find the possible values of Y. Construct a joint probability distribution table for X and Y. Include the marginal probabilities.

b) Find E(X) and E(Y).

c) Show that X and Y are not independent.

Given f(x) = 1 x 2 − 1 , f 0 (x) = −2x (x 2 − 1)2 and f 00(x) = 2(3x 2 + 1) (x 2 − 1)3 . (a) [2 marks] Find the x-intercept and the y-intercept of f, if any. (b) [3 marks] Find the horizontal and vertical asymptotes for the graph of y = f(x). (c) [4 marks] Determine the intervals where f is increasing, decreasing, and find the point(s) of relative extrema, if any. (d) [3 marks] Determine the intervals where f is concave up, concave down, and find the inflection point(s), if any. (e) [3 marks] Sketch the graph of f and label all important points.

Given the sample results:
Pop 1 Pop 2
x ̄1 = 54 x ̄2 = 50
s1 = 10.5 s2 = 11.0
n1 = 11 n2 = 16
(a) Find a 98% CI for μ1 − μ2.
(b) Perform the Hypothesis Test (α = 0.01) : H0 : μ1 = μ2; Ha : μ1 > μ2
(c) Explain how you could use part (a) to answer part (b).

We have the assignment (Buyer 1, Seller 1), (Buyer 2, Seller 2). The payoffs are:

Buyer 1 = 11

Seller 1 = 15

Buyer 2 = 10

Seller 2 = 6

Buyer 1 and Seller 2 can generate together 16. Buyer 2 and Seller 1 can generate together 26. Is the assignment stable?

1. Find an equation of the line that satisfies the given conditions.

Through (1/2, -2/3); perpendicular to the line 6x - 12y = 1

2. Find the slope and y-intercept of the line. Draw its graph.

4x + 5y = 10

3.  Find the x- and y-intercepts of the line. Draw its graph.

5x + 3y − 15 = 0

4. The equations of two lines are given. Determine whether the lines are parallel, perpendicular, or neither.

y = 4x + 4;  4y − 16x − 9 = 0

Suppose a production function is given by  F ( K , L ) = K^(1/2) L^(1/2), the price of capital “r” is $16, and the price of labor “w” is $16.
a. (5) What combination of labor and capital minimizes the cost of producing 100 units of output in the long run?
b. (5) When r falls to $1, what is the minimum cost of producing 100 pounds of pretzels in the short run? In the long run?
c. (5) When r falls to $1, will the cost of producing 100 units of output increase or decrease in the long-run? Explain.