essayreg: Linear Regression (Essay Question)

Exercise template for interpreting a simple regression based on randomly-generated data (with either a linear, semi-logarithmic, or log-log relationship) in form of an essay.

Name:

essayreg

Type:

string

Related:

essayreg2

Preview:

Consider the following regression results:


Call:
lm(formula = y ~ x, data = d)

Residuals:
     Min       1Q   Median       3Q      Max 
-2.14867 -0.82868 -0.07472  0.66596  2.54119 

Coefficients:
             Estimate Std. Error t value Pr(>|t|)
(Intercept) 0.0001676  0.1254992   0.001    0.999
x           1.2492437  0.1241613  10.061 2.04e-14

Residual standard error: 0.9786 on 59 degrees of freedom
Multiple R-squared:  0.6318,    Adjusted R-squared:  0.6255 
F-statistic: 101.2 on 1 and 59 DF,  p-value: 2.043e-14

Describe how the response y depends on the regressor x.

The presented results describe a linear regression.

The mean of the response y increases with increasing x.

If x increases by 1 unit then a change of y by about 1.25 units can be expected.

Also, the effect of x is significant at the 5 percent level.

Consider the following regression results:


Call:
lm(formula = y ~ x, data = d)

Residuals:
     Min       1Q   Median       3Q      Max 
-1.02232 -0.27147 -0.00678  0.25588  1.02013 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.05704    0.06948   0.821    0.415
x            0.52884    0.06511   8.122 8.17e-11

Residual standard error: 0.5106 on 52 degrees of freedom
Multiple R-squared:  0.5592,    Adjusted R-squared:  0.5507 
F-statistic: 65.96 on 1 and 52 DF,  p-value: 8.175e-11

Describe how the response y depends on the regressor x.

The presented results describe a linear regression.

The mean of the response y increases with increasing x.

If x increases by 1 unit then a change of y by about 0.53 units can be expected.

Also, the effect of x is significant at the 5 percent level.

Consider the following regression results:


Call:
lm(formula = y ~ x, data = d)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.3262 -1.0275 -0.0741  1.2578  4.4282 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)
(Intercept)  0.05518    0.25280   0.218   0.8282
x           -0.42237    0.23631  -1.787   0.0806

Residual standard error: 1.713 on 45 degrees of freedom
Multiple R-squared:  0.06629,   Adjusted R-squared:  0.04554 
F-statistic: 3.195 on 1 and 45 DF,  p-value: 0.08062

Describe how the response y depends on the regressor x.

The presented results describe a linear regression.

The mean of the response y decreases with increasing x.

If x increases by 1 unit then a change of y by about -0.42 units can be expected.

However, the effect of x is not significant at the 5 percent level.

Description:

The results of a linear regression model (linear, semi-logarithmic, or log-log) need to be interpreted in an essay. By adding the "exstringtype" metainformation "essay|file" for this "string" question, it is specified that an open-ended answer should be entered using a text editor and additionally a file can be uploaded. This type of extended string question is currently supported in Moodle and in QTI 2.1 (OpenOlat in particular). The details of the rendering in Moodle are additionally controlled through several "exextra" metainformation tags.

Solution feedback:

Yes

Randomization:

Random numbers and text blocks

Mathematical notation:

Yes

Verbatim R input/output:

Yes

Images:

Other supplements:

Template:

essayreg.Rmd

essayreg.Rnw

Raw: (1 random version)

essayreg.md

essayreg.tex

PDF:

HTML:

(Note that the HTML output contains mathematical equations in MathML, rendered by MathJax using ‘mathjax = TRUE’. Instead it is also possible to use ‘converter = “pandoc-mathjax”’ so that LaTeX equations are rendered by MathJax directly.)

Demo code:

library("exams")

set.seed(403)
exams2html("essayreg.Rmd", mathjax = TRUE)
set.seed(403)
exams2pdf("essayreg.Rmd")

set.seed(403)
exams2html("essayreg.Rnw", mathjax = TRUE)
set.seed(403)
exams2pdf("essayreg.Rnw")

Achim Zeileis 2017-08-14 TEMPLATES
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