True of False: The Chancellor of a university has commissioned a team to collect data on students’ GPAs and the amount of time they spend bar hopping every week (measured in minutes). He wants to know if imposing much tougher regulations on all campus bars to make it more difficult for students to spend time in any campus bar will have a significant impact on general students' GPAs. His team should use a regression analysis to test the significance of the slope.

False. They need to use a t test

See explanation below.

Step-by-step explanation:

False. They need to use a t test

Let's suppose that we have the following linear model:

Where Y is the dependent variable (GPA score) and X the independent variable (amount time students spend bar hopping). represent the intercept and the slope.  

In order to estimate the coefficients we can use least squares estimation.  

If we are interested in analyze if we have a significant relationship between the dependent and the independent variable we can use the following system of hypothesis:

Null Hypothesis:

Alternative hypothesis:

Or in other wouds we want to check is our slope is significant.

They need to apply a t test with the rehression analysis

In order to conduct this test we are assuming the following conditions:

a) We have linear relationship between Y and X

b) We have the same probability distribution for the variable Y with the same deviation for each value of the independent variable

c) We assume that the Y values are independent and the distribution of Y is normal  

The significance level is provided and on this case is assumed

The standard error for the slope is given by this formula:

Th degrees of freedom for a linear regression is given by since we need to estimate the value for the slope and the intercept.  

In order to test the hypothesis the statistic is given by:

The confidence interval for the slope would be given by this formula:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: