1. Consider the regression model: M] = ßo = ß1 × UR where MJ is the past-month marijuana-use rate for 12-17 year-olds in a state in 2009-10, UR is the average state unemployment rate for 2009-10, and there are 51 observations (50 states plus DC). The results are the following, with the standard errors in parentheses below the coefficient estimate: M] = 8.971 + 0.244 × UR (1.406) (0.148) a. Give the formal null and alternative hypotheses for whether the variable UR has a coefficient that is different from zero. b. Give the formal null and alternative hypotheses for whether the variable UR has a positive coefficient. c. Calculate the t-stat for the coefficient estimate on UR. d. Determine the critical values for the two-sided test on that coefficient for tests at the 1%, 5%, and 10% levels. Is the coefficient estimate statistically significant at each of those levels? e. Determine the critical value for the one-sided hypothesis test (at the 5% significance level) on that estimate to test if it is positive. What is the conclusion of the hypothesis test? f. Calculate the 95% confidence interval for the coefficient estimate on UR.
Family of Curves
A family of curves is a group of curves that are each described by a parametrization in which one or more variables are parameters. In general, the parameters have more complexity on the assembly of the curve than an ordinary linear transformation. These families appear commonly in the solution of differential equations. When a constant of integration is added, it is normally modified algebraically until it no longer replicates a plain linear transformation. The order of a differential equation depends on how many uncertain variables appear in the corresponding curve. The order of the differential equation acquired is two if two unknown variables exist in an equation belonging to this family.
XZ Plane
In order to understand XZ plane, it's helpful to understand two-dimensional and three-dimensional spaces. To plot a point on a plane, two numbers are needed, and these two numbers in the plane can be represented as an ordered pair (a,b) where a and b are real numbers and a is the horizontal coordinate and b is the vertical coordinate. This type of plane is called two-dimensional and it contains two perpendicular axes, the horizontal axis, and the vertical axis.
Euclidean Geometry
Geometry is the branch of mathematics that deals with flat surfaces like lines, angles, points, two-dimensional figures, etc. In Euclidean geometry, one studies the geometrical shapes that rely on different theorems and axioms. This (pure mathematics) geometry was introduced by the Greek mathematician Euclid, and that is why it is called Euclidean geometry. Euclid explained this in his book named 'elements'. Euclid's method in Euclidean geometry involves handling a small group of innately captivate axioms and incorporating many of these other propositions. The elements written by Euclid are the fundamentals for the study of geometry from a modern mathematical perspective. Elements comprise Euclidean theories, postulates, axioms, construction, and mathematical proofs of propositions.
Lines and Angles
In a two-dimensional plane, a line is simply a figure that joins two points. Usually, lines are used for presenting objects that are straight in shape and have minimal depth or width.
Please solve part d, e, and f.
![1. Consider the regression model: M] = ßo = ß1 × UR where MJ is the past-month marijuana-use rate
for 12-17 year-olds in a state in 2009-10, UR is the average state unemployment rate for 2009-10, and
there are 51 observations (50 states plus DC). The results are the following, with the standard errors in
parentheses below the coefficient estimate:
M] :
= 8.971 + 0.244 × UR
(1.406) (0.148)
a. Give the formal null and alternative hypotheses for whether the variable UR has a coefficient that is
different from zero.
b. Give the formal null and alternative hypotheses for whether the variable UR has a positive coefficient.
c. Calculate the t-stat for the coefficient estimate on UR.
d. Determine the critical values for the two-sided test on that coefficient for tests at the 1%, 5%, and
10% levels. Is the coefficient estimate statistically significant at each of those levels?
e. Determine the critical value for the one-sided hypothesis test (at the 5% significance level) on that
estimate to test if it is positive. What is the conclusion of the hypothesis test?
f. Calculate the 95% confidence interval for the coefficient estimate on UR.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fa3f39217-6130-4f13-a4f0-d29b129d90ed%2F8615382a-75f5-41f5-be10-1b6503917168%2Fd4h78i7_processed.png&w=3840&q=75)
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