Some college students critique professors teaching at ratemy

Some college students critique professors teaching at ratemyprofessors.com a web page where students anonymously rate their professors on quality, easiness, and attractiveness. using the self-selected data from this public forum, researches examine the relations between quality, easiness, and attractiveness for professors at various universities. in this exercise we will work with a portion of these data that the researchers made publicly available,

Solution

a) average beauty standarized score is -0.0883...average teaching evaluation score is 3.9983..
Intercept = 4.010....
so, 3.9983 = 4.010 + ( -0.0883* slope) i.e, slope = 0.1325028.....

b) from the scatterplot,and the q-q plot we can see with the increase in values of beauty also resulting in increase in values of evaluation and the line is sloping upward from left to right, thus the slope is positive......

c) Linear regression  needs at least 2 variables of metric (ratio or interval) scale. A rule of thumb for the sample size is that regression analysis requires at least 20 cases per independent variable in the analysis.

linear regression needs the relationship between the independent and dependent variables to be linear. It is also important to check for outliers since linear regression is sensitive to outlier effects. The linearity assumption can best be tested with scatter plots

the linear regression analysis requires all variables to be multivariate normal. This assumption can best be checked with a histogram and a fitted normal curve or a Q-Q-Plot. Normality can be checked with a goodness of fit test, e.g., the Kolmogorov-Smirnof test. When the data is not normally distributed a non-linear transformation, e.g., log-transformation might fix this issue, however it can introduce effects of multicollinearity.

linear regression assumes that there is little or no multicollinearity in the data. Multicollinearity occurs when the independent variables are not independent from each other. A second important independence assumption is that the error of the mean has to be independent from the independent variables.

Multicollinearity might be tested with

Correlation matrix – when computing the matrix of Pearson\'s Bivariate Correlation among all independent variables the correlation coefficients need to be smaller than 1.

inear regression analysis requires that there is little or no autocorrelation in the data. Autocorrelation occurs when the residuals are not independent from each other. In other words when the value of y(x+1) is not independent from the value of y(x). This for instance typically occurs in stock prices, where the price is not independent from the previous price.While a scatterplot allows you to check for autocorrelations, you can test the linear regression model for autocorrelation with the Durbin-Watson test.  

The last assumption the linear regression analysis makes is homoscedasticity. The scatter plot is good way to check whether homoscedasticity (that is the error terms along the regression are equal) is given.

from the plots given in the problem, all the conditions are satisfied!