12. Four research participants take a test of manual dexterity (high scores mean better dexterity) and an anxiety test (high scores mean more anxiety). The scores are as follows.
Person Dexterity Anxiety
1 1 10
2 1 8
3 2 4
4 4 –2
(a) Scatter Graph:
Scatter and Regression
Using an online calculator, we have 4 data pairs (x,y):
(1,10)
(1,8)
(2,4)
(4,-2)
Regression equation:
y = a + bx
y = 12.3 - 3.67x
This is the line of best fit. You can plot the scatter graph using the points above (x,y) to see how close the points are to the regression line.
I hope this helps and is what you were asking.
To create a scatter graph, we will plot the data points for each participant on a graph. The x-axis will represent the scores for manual dexterity, and the y-axis will represent the scores for anxiety.
First, let's list the data points for each participant:
Person 1: Dexterity = 1, Anxiety = 10
Person 2: Dexterity = 1, Anxiety = 8
Person 3: Dexterity = 2, Anxiety = 4
Person 4: Dexterity = 4, Anxiety = -2
Now we can plot these points on the graph. Choose a scale for each axis that allows you to clearly see all the data points. In this case, we can use a scale of 1 unit per grid line.
For Person 1, locate the point (1, 10) on the graph. For Person 2, locate the point (1, 8), and so on. Once you have plotted all four points, connect them with a line or smooth curve if possible.
To perform regression analysis on this data, we can find the line of best fit. This line represents the general trend in the data and can help us make predictions.
There are many software programs and calculators that can perform linear regression analysis for us, but here we will use a simple method to estimate the line of best fit. Start by drawing a straight line through the data points that appears to "fit" the data well. This line should roughly be in the middle of the scatter of points.
Next, estimate the slope and y-intercept of the line. The slope represents the change in the y-axis variable (anxiety) for every 1-unit increase in the x-axis variable (dexterity). The y-intercept represents the value of y (anxiety) when x (dexterity) is 0.
Once you have estimated the slope and y-intercept, write the equation of the line in the form: y = mx + b, where m is the slope and b is the y-intercept.
For example, if you estimated the equation of the line to be y = 2x - 6, this means that for every 1-unit increase in dexterity, anxiety increases by 2 units. The line intersects the y-axis at -6, indicating that when dexterity is 0, anxiety is -6 (note that negative anxiety values might not make practical sense in this context).
Remember, this is just an estimate of the line of best fit. The actual line of best fit may differ slightly depending on the statistical method used.
In summary, to create a scatter graph, plot the data points for each participant on a graph with the x-axis representing dexterity and the y-axis representing anxiety. Connect the points with a line or curve if possible. To perform regression analysis, estimate the line of best fit by drawing a straight line through the data points and calculating the slope and y-intercept.