Multiple linear regression I: as simple linear regression and more (F-test for model, t-test / confidence interval for one regression coefficient)

10 important questions on Multiple linear regression I: as simple linear regression and more (F-test for model, t-test / confidence interval for one regression coefficient)

What is multiple linear regression?

Multiple linear regression is a statistical technique for studying relationships, usually between quantitative variables. The variation in measurements on a response variable y is explained by variation in a number of x-variables

One y, multiple x

Waarvoor staat de epsilon in de formula for multiple regression?

De epsilon in de formula for multiple regression staat voor random error term. Random error term staat voor alles wat het model niet kan uitleggen, such as unknown variabels or natural randomness

What is the standard assumption in multiple regression?

Each observation has a random error term that is independent and normally distributed around zero with equal variance. I.i.d. Means independent and identically distributed
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What is the assumption for the systemic part in multiple regression?

The assumption for the systemic part in multiple regression als een
  • xx x-variabele verandert, verandert y steeds met ongeveer hetzelfde vaste effect.
  • What is sum of squared errors?

    Sum of squared errors the total amount of unexplained variation in a regression model. The sum of all squared differences between the observed values and the predicted values.

    What is TSS/SSR/SSE in a multiple regression model?

    TSS staat voor total sum of squares; totale spreiding in data
    SSR staat voor regression sum of squares; wat het model kan verklaren
    SSE: staat voor error sum of squares ; wat overblifjt als fout
    TSS = SSR + SSE
    SSR; verklaarde variate
    SSE: onverklaarde variatie

    What is the research question in a multiple regression model?

    The research question in a multiple regression model is: does the model have any predictive value?

    What betekent de coefficient of determination multiple R-squared?

    De coefficient of determination multiple r-squared geeft aan welk percentage van de variatie in y door alle x-variabelen samen wordt verklaard door het regressie model.

    Why should you use R squared adjusted in r squared?

    Adjusted R-squared is een aangepaste versie van R2R^2 R 2 die corrigeert voor het aantal voorspellers in het model, zodat je niet “oneerlijk” hoger scoort door simpelweg meer xx x-variabelen toe te voegen.

    What is overfitting in statistics?

    "the production of an analysis that corresponds too closely or exactly to a
    particular set of data, and may therefore fail to fit to additional data or predict future
    observations reliably“

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