BUSN final stand

Take the natural log of the monthly prices as the dependent variable.

what do you do if constant variance has been violated? (HW9 Q8)

-1

what is the derivative of negative x?

These observations possess a large difference between the true y values and the predicted values of y.

what is true of outliers

under 10

what number should your VIFs be at to indicated that collinearity is not an issue?

left side of graph, so sometime you have to do 1-norm.dist if looking for amount of people who scored above something.

what portion of the graph does norm.dist measure?

ok

when doing stat questions from HW 6 if you are asked for a whole number always round down

ok

when taking a BUSN test always double check your units

ok

when you are asked to give a CI and you are given a data set just use regression tools to generate a CI also don't forget to adjust your CI to the respective unit of measurement

1. find first derivative (f') 2. find 0's or DNE 3. plug critical values and 0's or DNEs into first derivative (f') 4. find y's by plugging x's into original equation (f(x))

(BUSN4000) finding relative max or min

1. find f' 2. find 0's or DNEs 3. plug critical values back into OG equation 4. Xs and Ys are intuitive (step 3 gives y, step 2 gives x)

(BUSN4000) how to find absolute max and min

1. find 2nd derivative (f") 2. plug critical values into second derivative, sign placement determines concavity

(BUSN4000) steps to finding concavity points or inflection points

just find where y is equal to 3 on the graph then figure what the x value is for that number and that is the answer

(b) Find the value of x for which f(x) = 3 and f(x) = 0. (i) f(x) = 3

H0: 𝛽1 = 1 Ha: 𝛽1 ≠ 1 H0: The average increase in overhead for a 10,000 unit increase in production is $1,000. Ha: The average increase in overhead for a 10,000 unit increase in production is not $1,000.

(c) Test whether or not the average increase in overhead cost for a 10,000 unit increase in production is different from $1,000.

H0: 𝛽3 = 11 Ha: 𝛽3 ≠ 11 H0: The average increase in monthly salary for a 1 month increase in seniority is $11 after accounting for the effects of the other explanatory variables in the model. Ha: The average increase in monthly salary for a 1 month increase in seniority is NOT $11 after accounting for the effects of the other explanatory variables in the model. Do not reject the null hypothesis: The average increase in monthly salary for a 1 month increase in seniority may be $11.

(c) The Associate HR Director believes that for each additional month an employee has been with the bank (TIME), their monthly salary increases by $11.

1.364=se When using this model to make predictions, we expect to be off by _______ units, on average.

(c) What would be a typical size error of prediction when you use this regression model? -1.364 Choose the correct interpretation of the typical size error of prediction you identified above by mentally inserting the value into the blanks below.

error residual x DF y

(d) What are the error degrees of freedom of the model fit? (Enter your answer as a whole number.)

experimental study

-controlled environment -randomization - there IS a causal link - If the company analysts observe a high R2 for the model predicting internet usage time using educational level, then the company can conclude that there exists a causal link between educational level and time on the internet. -This is an experimental because vehicles were replicated within each treatment condition. (HW12 Q 2)

observational study

-lack of randomization - we observe and do not control - no causal link - If the company analysts observe a high R2 for the model predicting internet usage time using educational level, then the company still cannot conclude that there exists a causal link between educational level and time on the internet.

no (so if your elasticity is negative you messed something up)

BUSN: can elasticity be negative?

(OR - 1 ) * 100 Or =exp(x)

Compute the percent increase/decrease associated with the variable

-This includes a model with no explanatory variables and only the intercept (i.e., the mean model) -This includes 1 model with all explanatory variables. -This includes 6 1-variable models.

Data on 1,470 cars were obtained from the October 2002 issue of Road & Track: The New Cars. The following variables were available in order to predict selling price (y): -weight, in pounds (WEIGHT) -mileage in city driving (CITYMPG) -mileage in highway driving (HWYMPG) -horsepower, @ 6300 rpm (HP) -number of cylinders (CYLIN) -displacement, in liters (LITER) For the number of models you found above, which of the following statements are true? (Select all that apply.)

To determine the domain, we have to consider limitations on what values can be plugged into the previous function. Firstly, demand cannot be negative for either dictionary, so we need x ≥ 0 and y ≥ 0. Similarly, neither price can be negative, so we must have p = 21 - 0.008x - 0.002y ≥ 0 and q = 13 - 0.002x - 0.003y ≥ 0.

Find the domain of the function R(x, y).

a. 4 * -.213 = -.852 ->2nd -> ln *1.58 b. 1.58 X -.213 = .33654 -> -.213 X 4 = -.852 -> 2nd -> ln = .426561 X .33654 ANSWER B WILL BE NEGATIVE FOR THIS PARTICLAR PROBLEM

HW 6 Q 7 that one stupid e problem with the calculator After its fastest rate of growth ever during the 1980s and 1990s, the rate of growth of world population is expected to slow dramatically in the twenty-first century. The function G(t) = 1.58e−0.213t gives the projected annual average percent population growth per decade in the tth decade, with t = 1 corresponding to 2000.† (a) What will the projected annual average population growth rate be in 2030 (t = 4)? (Round your answer to two decimal places.).67 0.67 % per decade(b) How fast will the projected annual average population growth rate be changing in 2030 (t = 4)? (Round your answer to two decimal places.)-.14 -0.14 % per decade per decade

just type whatever r^2 is

How much variation in absenteeism (or any other response variable) has been explained? (HW 8 Q 7 )

blocking

If the company had grouped similar vehicles together and then randomly assigned vehicles to treatment groups within each group, this would have been an example of which principle of design?

CP is given number P is amount of coefficients + 1 (K+1) the bigger the discrepancy the higher propensity of important variable being omitted

Model #9 has a large bias component because of the large discrepancy between Cp and p.

=exp (X)

OR odds ratio excel calculation

which implies that P'' at this critical number is *greater than* 0, so the critical number gives a *minimum* value of P.

P" (t) = .31 (HW 6 Q3)

x^2 test logistic regression =1/1+(EXP(-H57))

P(Y = Retail) = 1 / b0+b1+b2... what kind of test are we doing?

see t-test for coefficient of x^4

Perform the appropriate statistical test to test whether the fourth-order model explains a statistically significant amount of variation in total weekly cost above and beyond of that explained by the third-order model.

P(x) * x

R(x)

(b) The assumption of normally-distributed disturbances. (c) H0: Disturbances are normal Ha: Disturbances are non-normal

Shapiro Wilkes test (b) What is being tested here? (c) Which hypotheses are being tested?

The standard error of a prediction of a single value is *larger than* the standard error of a prediction of a conditional mean.

State why the prediction interval is wider than the confidence interval. (HW9 Q1)

a. This measures the average rate of change in revenue as the expenditure changes from a thousand dollars to b thousand dollars. The units are thousands of dollars per thousands of dollars. b. This measures the instantaneous rate of change in the revenue when x thousand dollars are spent on advertising. The units are thousands of dollars per thousands of dollars. c. 4000

Suppose that the total revenue realized by the Odyssey Travel Agency is R = f(x) thousand dollars if x thousand dollars are spent on advertising. (a) What does f(b) − f(a) / b − a measure, what are the units? (b) What does f '(x) measure? Give units. (c) Given that f '(20) = 4, what is the approximate change in the revenue if Odyssey increases its advertising budget from $20,000 to $21,000?

(c) H0: 𝛽1 = 0 Ha: 𝛽1 ≠ 0 Ho: There is no linear relationship between participation rate and match rate after accounting for the effects of the other explanatory variables in the model. Ha: There is a linear relationship between participation rate and match rate after accounting for the effects of the other explanatory variables in the model.

Test the significance of match rate in determining participation rate after accounting for the effects of all the other explanatory variables (testing one variable against other variable) (c) Test the significance of match rate in determining participation rate after accounting for the effects of all the other explanatory variables. Interpret the hypotheses you specified above.

bigger smaller

The ___ r^2 adjusted the better The ___ Standard error the better

This is most likely the result of a multicollinearity problem with the model. This is likely because bedrooms, bathrooms, and living area are all roughly measuring the same thing: The size of the property.

The coefficient for BEDROOMS is negative, which seems counterintuitive. Choose the BEST explanation for this result.

experimental control

The fact that the company measured emissions in a laboratory setting where other sources of variation were eliminated, is an example of which principle of design?

The dollar value of Nancy's holdings *at* time t.

The number of AAPL shares that Nancy owns at time t is given by f(t). The price per share of the stock of AAPL at time t is g(t) dollars. What does the function f(t)*g(t) represent?

H0: 𝛽1 ≥ 90 Ha: 𝛽1 < 90

The regression coefficient for EDUC from this model is an estimate of the average increase in monthly salary for every additional year of education (while holding all other variables fixed). Based on your analysis, can we conclude that the actual average increase in monthly salary for every additional year of education is less than $90? Use a 10% level of significance.

the unit cost of the commodity at time t

The total cost incurred by time t in the production of a certain commodity is f(t) dollars. The number of products produced by time t is g(t) units. What does the function f(t)/g(t) represent?

norm.inv(.8,155,25)

What is the least amount of money you need to spend on groceries each week to be in the top 20% of the distribution? (Answer as a whole number.) mean = 155 SD = 25

sqrt(.005) [MS y residual x in given data set]

What is the typical size of a prediction error from this model? (HW 7 Q 8F)

how ever many variable are in the model + 1 (K+1) -so if model is showing Finance and Prod the answer would be 3

What value of p should be used when using Cp to evaluate Model #9? (Enter your answer as a whole number.)

sort by cook's D largest wins

Which data point is most influential on the regression line due to extremity in both y and x dimensions.

look at observation with biggest cook's D (sort)

Which data point is most influential on the regression line due to extremity in both y and x dimensions?

sort by leverage (BUSN Reg advanced settings tab selection)

Which observations have the potential to affect the regression line due to extreme placement on the x-axis, but may not necessarily exert undue influence on the line?

sort by leverage largest wins

Which observations have the potential to affect the regression line due to extreme placement on the x-axis, but may not necessarily exert undue influence on the line?

cross sectional data

data on multiple analysis units (teams) measured at a single point in time

K-L , N-K-1 Fstat, K-L , N-K-1

fill in the blanks: F = (____ , _____) F.DIST.RT (X,X,X) -this is how you find f statistic in excel

time series data

have data on a single analysis unit (a company) measured at multiple points in time

do busn reg advanced tab and click tests of normality in the bottom right. W

how do you do shapiro wilkes test in excel? What is the name of the test variable?

t.dist(-t stat, DF, true) *2 (unless one sided test) VERY IMPORTANT TO MAKE T STATE NEGATIVE AND MULTIPLY BY TWO

how do you find p-value in excel?

1. find f' 2. find 0's or DNEs 3. plug critical points into first derivative

how to find where function is increasing or decreasing

ok

if given a data set and asked for a CI just use regression analysis if you are not given a data set use coefficient +- (t.inv * standard error) ---remember to cut probability and multiply by negative 1 for t.inv calculation.

-less collinearity -more collinearity

lower VIF (variance inflation factor) indicates: higher VIF (variance inflation factor) indicates:

panel data

multiple analysis units over multiple points in time

ok

only use general power rule when numerator is not a function

ss regression / ss total

r^2 equation (HW8Q1)

actual - expected underestimate, overestimate

residual equations (BUSN) positive residual indicates: X units below the actual value negative residual indicates: X units above the actual value

H0: 𝛽1 = 𝛽2 = 0 Ha: At least one of the coefficients is not equal to 0 H0: None of the explanatory variables are important in explaining/predicting Y .Ha: At least one explanatory variable is important in explaining/predicting Y

test the overall fit of the model

ok

the derivatives of negative exponents create negative funcitons (2x^-3 = -6x^2)