Exercise insights

Question 1

How do you calculate correlation in libre office calc

Answer 1

Mark the columns you want to correlate. In header click Data -> Statistics -> correlation. Otherwise you can use the correl function.

Question 2

Why is the correlation coefficient not the slope of an estimated line of equation for the relationship between two variables

Answer 2

Because the correlation coefficient is a measure of the strength of their relationship aka how well you can make a line of the scattered dots not how that line points, that is the job of the regression line.

Question 3

Is the concept of dependent and independent variables related to correlation or regression

Answer 3

Regression

Question 4

Is correlation a measure of how large the covariance is between two variables

Answer 4

Yes

Question 5

How do you get the estimated slope coefficient of two variables in libre office calc

Answer 5

From the header you click Data -> Statistics -> Regression, you then mark the dependent and independent variable and where you want the result wereafter you get the slope coefficient under Coefficients next to X1 if you only have two variables.

Question 6

What does it mean when we say that the estimated slope coefficient is statistically significant.

Answer 6

That there is strong evidence that the relationship between the independent variable and the dependent variable in a regression model is not due to random chance. A relationship is statistically significance if the p-value is low and there is no third factor that influences both

Question 7

Can a regression model as a whole be statistically insignificant

Answer 7

Yes if the independent variables do not collectively explain a significant portion of the variation in the dependent variable. This can be due to a small sample size, noise in the data, a strong correlation between the independent variables or simply a weak relationship between the independent variables and the dependent ones.

Question 8

What happens when the slope coefficient is equal to zero

Answer 8

It means there is no relationship between the variables detectable with a regression model.

Question 9

If the p-value is high and the t-value is low is the relationship statistically significant

Answer 9

No if the t-value is high it indicates a strong relationship between the variables and when the p-value is low it means that the chance of observing such a t-value under the null hypothesis is very small. So if the t-value is high and the p-value is small it means that the null hypothesis of b being 0 is probably false and the model is statistically significant.

Question 10

How do you insert a trend line and function in a scatter plot in libre office calc

Answer 10

You create a scatter plot by marking the related columns and clicking the chart icon were-after you choose scatter-plot. Then after you have made your scatter-plot you can right click on the dots you want a trend-line of and choose trend line and function in the drop-down menu.

Question 11

The residual is the diference between the average dependent variable and the declared dependent varaible

Answer 11

No, thats the variance of that instance. The residual is the diference between the prediction of the estimator and the actual value at that point.

Question 12

In a quadratic regression model the deriviative can be interpreted as the increase when x changes by one unit

Answer 12

True

Question 13

In a linear probability model one can count on the model being restricted between 0 and 1

Answer 13

False, lines continue to infinity

Question 14

In which regression models does B1/100 represent a UNIT change in y at a 1% change in x. Linear, log-log, exponential or logarithmic

Answer 14

Only logarithmic

Question 15

In the log log model the coeficient is…

Answer 15

The expected percentage change in y when x changes by 1%

Question 16

If the correlation is -0.87 and one variable increases by 1 the expected change in the other variable is -0.87

Answer 16

False becouse correlation does mesure their relationship but the strength of their covariance. The only thing we get is that the relationship is a strong negative one.

Question 17

If the given regression model is y = b1x + b2x + b3x + b0 + e how do you make a restricted function for a restriction test

Answer 17

y = b1(x1+x2) +b3x + b0 + e

Question 18

If you answer that one is 2.5 percent likelyer for each year in education to be employed in a linear regression question why are you automatically wrong

Answer 18

Becouse percentage changes implies a logarithmic relationship. Name percentage points instead.

Question 19

How do you write a hypothesis test of joint significance

Answer 19

H0: B1 = B2… Bn = 0
HA: any B value is not 0

Question 20

How does the logit model look, what if the beta is 0.5

Answer 20

the logit model looks like an s and if the beta is 0.5 that is what multiplies the exponentiation both in the top and the bottom

Question 21

What assumptions of the OLS estimator is required for it to be unbiased

Answer 21

It needs to be linear in the parameters, it needs to fufill E(u|x) = 0 and it needs to lack perfect collinearity.

Question 22

What assumptions of the OLS estimator is required for the standard error and thus T and F tests to be valid.

Answer 22

That the samples shuld be independent from an identical distribution i.i.d and that there should be no large outliers.

Question 23

What assumptions is required for the OLS estimator to be BLUE the best linear unbiased estimator

Answer 23

it needs the errors to be homoskedastic for the Gaus Markov theorem to hold true and it needs the errors to be normally distributed

Question 24

Is the law of large numbers about consistency

Answer 24

Yes, and consistency means that the probability of the expected value of the estimator being that of the population approaches 1 as the sample size increases

Question 25

The central limit theorem is about consistency

Answer 25

No its about the distribution aproaching normal as the sample size increases.

Question 26

i.i.d leads to consistency

Answer 26

True

Question 27

What makes an estimator good

Answer 27

It is unbiased E(sample) = E(population, it is consitents E(E(sample) = E(population)) -n-> 1, an dit is efficient. var = small

Question 28

What may cause E(u|X) = 0 no endogineity to not hold

Answer 28

If there is correlation, or non linear relation between x and the residual or if there is a third factor that influences them both

Question 29

If you want your estimator to be efficient should you pick a sample with a larger or smaller variance

Answer 29

A larger variance becouse the variance of b decreases with the variance of X. It also decreases with the variance of n

Question 30

The requirement for an omitted variable to cause bias is

Answer 30

Correlation with model variables and an effect on the response variable

Question 31

What is an idea randomized controlled experiment

Answer 31

Ideal as subjects follow protocol perfectly. Randomized as i.i.d sampling. Controlled as having a control group for an effect without a cause. And lastly an experiment where people are not vaulentearing which would cause selction bias and reverse causality.

Question 32

What will large but imperfect multicolinearity lead to

Answer 32

Large standard errors for one or more of the regressors

Question 33

How can you make the OLS estimator be as good as possible. Make it artificially BLUE

Answer 33

You can use robust stadard errors for the gauss markov theorem to hold by nullifying the advers effect of heteroskedacity and you can rely on the central limit theorem to make the errors normally distributed when n is large.

Question 34

are the coefficients in a multiple regression model generally independently distributed

Answer 34

No they are not as they often are somewhat correlated their effect on y becomes muddled.

Question 35

F test assumes homoskedasity

Answer 35

True

Question 36

How do you make a hypothesis test to check if a relation is polynomial of a higher order than one.

Answer 36

You make an F test on the higher order variables.

Question 37

Can adding a non-linear regressor introduce multicolinearity

Answer 37

Yes although it is often not perfect as the relation is not linear although an F-test might be needed.

Question 38

What is probit

Answer 38

Using the cumulative normal distibution function to check the likelyhood of Y being zero dependent on x. Pr(Y=1|x) = C(b0+b1x). b0+b1x is the z-value

Question 39

logit gives similar results to probit

Answer 39

True

Question 40

Is R² menaingful in probability models

Answer 40

No