Question

1. Distinguish between the following:

1. Heteroskedasticity and autocorrelation
2. specified regression model vs estimated regression equation
3. data type vs level of measurement
4. ANOVA and Multiple Regression
5. Outliers vs Influencers
6. Distinguish between the following:
7. Heteroskedasticity and autocorrelation
8. specified regression model vs estimated regression equation
9. data type vs level of measurement
10. ANOVA and Multiple Regression
11. Outliers vs Influencers

Answer 1

1.

Heteroscedastisity refers to the case when the variability of the random disturbance is different for different components of the vector i.e. a random disturbance term {\displaystyle \epsilon _{i}} $\epsilon _{i}$ that has mean zero and standard deviation of {\displaystyle \sigma _{i}} $\epsilon _{i}$

Autocorrelation in regression refers to the non zero correlation between the different components of random distubances i.e. Cov( e_i, e_j​​​​​​) is not 0.

b.

Estimated regression equation shows the equation for y hat i.e. the predicted y on the basic of estimated regression coefficients. For instance, y hat= b0 + b1 * x.

On the other hand, specified regression model is the equation for actual values of y. It is based on population regression coefficients and error terms. For instance, y = βo + β1 * x + e

C.

A data type, specially in programming, is a classification that specifies which type of value a variable can take, for eg. Integers, floating point, character, strings, array etc.

Level of measurement or scale of measure is a classification that describes the nature of the data under consideration. There are 4 levels of measurement - nominal, ordinal, ratio, interval.

D.

Multiple Regression is the statistical model that we use to predict a continuous outcome on the basis of two or more continuous predictor variables using some mathematical equation, such as predicting the speed of a vehicle on the basis of fuel consumption.

ANOVA is the statistical technique that we use to analyze the differences among the population mean of a continuous variable that depends on one or more categorical variables, such as average yield of a crop depending on different fertilisers.

E.

An outlier is a data point that differs significantly from other observations, may be due to variability in the measurement or experimental error. They differ significantly from the overall pattern of the data.

Infuencers are the points in the sample that when removed can significantly change the slope of the regression line. The influencers can be seen as very extreme outliers.