Bivariate Correlation and Regression A researcher is studying which variables have an effect on the number of face-to-face interactions we have with friends. She hypothesizes that one of the most important variables will be a person’s age; older people may be less likely to use electronic forms of communication, and more likely to see their friends face-to-face. The researcher randomly sampled 6 people, and gathered the following data: Age Number of face-to-face interactions with friends per week 25 14 56 21 31 17 67 28 45 19 65 29 First things first: Identify the Independent and Dependent Variables: IV = DV = Now, visualize the data. Draw a scatterplot of these data below, making sure to label the axes. Calculating the regression equation: Find the means of the two variables: Y̅ = X̅ = Step 2: Construct your Computation Table: X (X - X̅) Y (Y - Y̅) (X - X̅)(Y - Y̅) (X - X̅)2 (Y - Y̅)2 Calculate b, the slope of the regression equation: Calculate a and write the completed equation:
Bivariate
A researcher is studying which variables have an effect on the number of face-to-face interactions we have with friends. She hypothesizes that one of the most important variables will be a person’s age; older people may be less likely to use electronic forms of communication, and more likely to see their friends face-to-face. The researcher randomly sampled 6 people, and gathered the following data:
|
Age |
Number of face-to-face interactions with friends per week |
|
25 |
14 |
|
56 |
21 |
|
31 |
17 |
|
67 |
28 |
|
45 |
19 |
|
65 |
29 |
First things first: Identify the Independent and Dependent Variables:
IV = DV =
Now, visualize the data. Draw a scatterplot of these data below, making sure to label the axes.
Calculating the regression equation:
Find the means of the two variables:
Y̅ =
X̅ =
Step 2: Construct your Computation Table:
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X |
(X - X̅) |
Y |
(Y - Y̅) |
(X - X̅)(Y - Y̅) |
(X - X̅)2 |
(Y - Y̅)2 |
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Calculate b, the slope of the regression equation:
Calculate a and write the completed equation:
Now, calculate r:
r =
What does r
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r-value |
Strength of relationship |
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0 |
No relationship |
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± 0.1 |
Very weak |
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± 0.2 |
Weak |
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± 0.3 |
Weak to moderate |
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± 0.4 |
Moderate |
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± 0.5 |
Moderate |
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± 0.6 |
Moderate to strong |
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± 0.7 |
Strong |
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± 0.8 |
Strong |
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± 0.9 |
Very strong |
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± 1 |
Perfect |
Calculate r-squared:
r2 =
What does all of this mean? Write up a brief interpretation of your regression equation and the r and r-squared measures you have calculated in the context of this research question.
Based on the results of your regression equation, if a person was 40 years old, how many face-to-face interactions with friends would you expect them (on average) to have in one week (please write your answer in a complete sentence)?
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