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Further Regression Analysis

sophie waddington 13 questions

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Questions in this quiz (13)

  1. 1Simple Linear Regression
    - we assumed that errors about the line are [blank_start]normally[blank_end] distributed with mean [blank_start]0[blank_end] and constant variance > we now see how to check whether these assumptions are valid

    correlation
    - linear regression - predict [blank_start]response[blank_end] variable (Y) without our explanatory variable (X)
    - we can predict the response variable with the equation of a [blank_start]straight[blank_end] line
    - alpha = intercept, where the line crosses the [blank_start]y[blank_end] axis
    - beta = coefficient of explanatory x, the [blank_start]slope[blank_end] of the line
    - epsilon = errors    Image for question 1
    1. Anormally
    2. B0
    3. Cresponse
    4. Dstraight
    5. Eslope
    6. Fy
  2. 2IN minitab
    - we can fit a straight line using > stat > regression > fitted line plot
    - we select our y-variable (male lobster weight for example, the [blank_start]response[blank_end] variable we are trying to predict), and our x-variable (male lobster length, the predictor/explanatory variable)
    - we are trying to predict the weight of our lobsters by the [blank_start]length[blank_end] of our lobsters
    - we click on graphs, click four in one and select standardise [blank_start]residuals[blank_end]

    output
    - focus on top 2 plots = check normality = errors should fit the line, variance = should be evenly scattered around [blank_start]0[blank_end]

    if there is a problem with either of the plot, then we need to consider a different model    Image for question 2
    1. Aresponse
    2. Blength
    3. Cresiduals
    4. D0
  3. 3Interpretation of female lobsters
    - the normality plot is fine, but the plot of the [blank_start]residuals[blank_end] against the fitted values has a pattern > above the line, below the line, above the line; suggesting a more complex model might fit better

    a better model might be a [blank_start]quadratic[blank_end] curve...fitting a quadratic model    Image for question 3
    1. Aresiduals
    2. Bquadratic
  4. 4A [blank_start]quadratic[blank_end] model: more complex model
    - still using same x variable (female length)
    - instead of just having intercept, [blank_start]slope[blank_end], and error term we also have an extra term
    - X^2 which will give the curve

    stat > regression > fitted line plot
    Image for question 4
    1. Aquadratic
    2. Bslope
  5. 5Minitab provides an analysis of variance table: doing hypothesis tests
    - linear term and quadratic term
    - the crucial term for deciding if you need a quadratic model is the p value for the quadratic term
    - if the p value is [blank_start]big[blank_end], we do not need a quadratic term
    - if the p value is [blank_start]small[blank_end], we do need it, the quadratic term significantly improves the fit of the line

    Big p value = we do not that term

    P = 0.016 < 0.05 (always test at the [blank_start]5[blank_end]% significance level), so we do need this quadratic term

    Image for question 5
    1. Abig
    2. Bsmall
    3. C5
  6. 6[blank_start]Influential[blank_end] points
    - a small number of points can have a big effect on regression lines
    - e.g. a very small, very short lobster
    - can remove these points and retest

    as the p value is now big (0.149 > 0.05) the quadratic term does [blank_start]not[blank_end] significantly improve the fit to the data, and a straight line should be used
    - having removed the quadratic term, you must fit the simpler model and check the residuals    Image for question 6
    1. AInfluential
    2. Bnot
  7. 7Extra predictor variables
    - we have seen how we can see if we need a quadratic term, similarly, if there are several possible [blank_start]predictor[blank_end] variables e.g. temperature, humidity etc. we can see which ones are needed by looking to see if they significantly improve the fit
    - we can use sequential ANOVA or [blank_start]t[blank_end]-tests on the fitted coefficients to decide what terms to include
    - for example, log urate in the blood of men was thought to be related to BM1, alcohol consumption and age
    - we use STAT > REGRESSION > REGRESSION > FIT REGRESSION MODEL
    we thus imput log urate as the response and BMI, alcohol and age as continous predictors

    trying to predict log of urate using
    - BMI
    - alcohol consumption
    - age

    [blank_start]response[blank_end] = think we are trying to predict, continuous predictors = things we are changing
    1. Apredictor
    2. Bt
    3. Cresponse
  8. 8Multiple Regression Example
    - p-values test if any of these coefficients are significantly different from [blank_start]0[blank_end] or not
    - we need to look for big p values e.g. Age = 0.612 > 0.05 ([blank_start]5[blank_end]% significance level)
    - age is not helping us predict log urate > age does [blank_start]not[blank_end] improve the prediction of log urate in males (its coefficient is not significantly different from 0)
    - age should be removed (or any coefficients with p values above 0.05) and the model refitted
    - this gives

    gives [blank_start]regression[blank_end] equation again = intercept term + BMI male + alcohol male

    as the p values for BMI and alcohol are both very [blank_start]small[blank_end] (P<0.001) both are important in predicting log urate levels in men (i.e. there coefficients are significantly different from 0)
    - as both coefficients are [blank_start]positive[blank_end], we see that log urate increases as BMI increases and as alcohol consumption [blank_start]increases[blank_end]    Image for question 8
    1. A0
    2. B5
    3. Cnot
    4. Dregression
    5. Esmall
    6. Fpositive
    7. Gincreases
  9. 9Comparison of Regression Lines
    - why might you want to compared [blank_start]regression[blank_end] lines?
    - if we fit straight lines in male and female lobsters (reduced data set, influential point of small female taken out) for weight against length we can ask:

    > are the slopes significantly [blank_start]different[blank_end]
    > are the intercepts significantly different

    1. Aregression
    2. Bdifferent
  10. 10How do we compare regression lines: stack all the data all in one column
    - this plot suggests the intercepts are different but the slopes may [blank_start]not[blank_end] be
    - to compare the lines, we [blank_start]stack[blank_end] the column so that all the weights are in one column (male and female) and all the lengths in another
    - we generate a new column (sex) which is [blank_start]0[blank_end] for males and 1 for females
    - we generate another column (an interaction between sex and length) > zero for males and length for females (female length); it only exists the lobster is female
    - we first fit length and sex > this fits different intercepts and a common slope (i.e. parallel lines)
    - we input weight as our response, length as a continuous predictor and sex as a categorial variable    Image for question 10
    1. Anot
    2. Bstack
    3. C0

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Description
Stats Quiz on Further Regression Analysis, created by sophie waddington on 09/01/2019.
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