Skip to main content
Statistics LibreTexts

14.10: Correlation Exercises

  • Page ID
    18130
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)

    Exercise \(\PageIndex{1}\)

    What does a correlation assess?

    Answer

    Correlations assess the strength and direction of a linear relationship between two quantitative variables.

     

    Exercise \(\PageIndex{2}\)

    What sort of relation is displayed in the scatterplot in Figure \(\PageIndex{1}\) below?

    Scatterplot with weak relation generally going up and to the right.
    Figure \(\PageIndex{1}\): Sample Scatterplot. (CC-BY-NC-SA Foster et al. from An Introduction to Psychological Statistics)
    Answer

    Strong, positive, linear relation 

    Exercise \(\PageIndex{3}\)

    Create a scatterplot from the following data:

    Table \(\PageIndex{1}\)- Raw Data
    Hours Studying Overall Class Performance
    0.62 2.02
    1.50 4.62
    0.34 2.60
    0.97 1.59
    3.54 4.67
    0.69 2.52
    1.53 2.28
    0.32 1.68
    1.94 2.50
    1.25 4.04
    1.42 2.63
    3.07 3.53
    3.99 3.90
    1.73 2.75
    1.9 2.95
    Answer

     

    Scatterplot showing weak relationship but that generally goes up and to the right.
    Figure \(\PageIndex{2}\): Scatterplot of data from Table \(\PageIndex{1}\). (CC-BY-NC-SA Foster et al. from An Introduction to Psychological Statistics)

     

    Exercise \(\PageIndex{4}\)

    Using the data from Table \(\PageIndex{1}\), test for a statistically significant relation between the variables.

    Answer

    Step 1:

    Research Hypothesis:  “There is a positive linear relation between time spent studying and overall performance in class.”

    Null Hypothesis “There is no liner relation between time spent studying and overall performance in class.” 

    Step 2: \(df = 15 – 2 = 13, \alpha = 0.05, r_{Crit} = 0.514\).

    Step 3: Using the Sum of Products table, you should find: \(\overline{X_{HS}} = 1.65, \overline{X_{OCP}}= 2.95, r = 0.65\).  [Your means might differ due to rounding differences.

    Step 4: Obtained statistic is greater than critical value, reject \(H_0\). There is a statistically significant, strong, positive relation between time spent studying (\(\overline{X_{HS}} = 1.65) and performance in class (\overline{X_{OCP}}= 2.95), \(r(13) = 0.65, p < .05\).  This supports the research hypothesis.  

    Contributors and Attributions

    • Foster et al. (University of Missouri-St. Louis, Rice University, & University of Houston, Downtown Campus)


    14.10: Correlation Exercises is shared under a CC BY-NC-SA license and was authored, remixed, and/or curated by Michelle Oja.

    • Was this article helpful?