Day 10 Influential Points Activity

Does the age at which a child begins to talk predict a future score on a test of mental ability?

A study of the development of young children recorded the age in months at which each of 21 children spoke their first word and the Gesell Adaptive Score, the result of an aptitude test taken much later.

The data is shown below.

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We will be determining the relationship to see if Age at First Word can predict the Gesell Score.

Enter the age data into L1 and the Gesell Score into L2 (Stat, Edit).

4

With the data in L1 and L2, create a scatterplot showing the relationship between age and Gesell Score.
Use Statplot (2nd, y=).
Describe the relationship between age at first word and Gesell Score:
Select all answers that apply.

4

Do a linear regression (Stat, Calc, #8) to calculate the correlation coefficient.
Enter the value rounded to three places past the decimal point.
Be careful to note the sign.

4

Use the linear regression information to create a Linear Model Equation for predicting Gesell Score based on Age at First Word.
Match the numbers and variables with the correct description.

Stavka koja se može prevući		Odgovarajuća stavka
Age at First Word (in months)		Slope: ___________ points/month
-0.640		Intercept: _________ points
Gesell Score		Explanatory Variable
109.874		Response Variable
-1.127		Correlation Coefficient

4

Enter the Linear Model Equation for predicting the Gesell Score based on the Age at First Word:
Use the correct notation (-hat) and meaningful words.
Use 'Age' and 'Score' for the explanatory and response variables in the equation.
Slope and intercept should be rounded to three places past the decimal point.
No spaces.

4

Explain the meaning of the slope in this context.
Correct the answer below:

A toddler 's predicted Gesell Score goes down by 1.127 points for each month older that they are when they speak their first word.

A toddler who speaks at 0 months has a predicted Gesell Score of -0.640

A toddler's predicted Gesell Score goes down by 0.640 points for each month older that they are when they speak their first word.

A toddler who speaks at 0 months has a predicted Gesell Score of 109.874 points.

A toddler's predicted Gesell Score goes up by 1.127 points for each month older that they are when they speak their first word.

A toddler who speaks at 0 months has a predicted Gesell Score of -1.127 points.

4

Explain the meaning of the intercept in this context.
Correct the answer below:

A toddler who speaks at 0 months has a predicted Gesell Score of -0.640

A toddler 's predicted Gesell Score goes down by 1.127 points for each month older that they are when they speak their first word.

A toddler's predicted Gesell Score goes up by 1.127 points for each month older that they are when they speak their first word.

A toddler's predicted Gesell Score goes down by 0.640 points for each month older that they are when they speak their first word.

A toddler who speaks at 0 months has a predicted Gesell Score of 109.874 points.

A toddler who speaks at 0 months has a predicted Gesell Score of -1.127 points.

4

Now that your data is in L1 and L2, check the Linear Model Equation by graphing the Residual Plot.
1. Do a linear regression, Stat, Calc, #8, Store the Regression Equation (Store RegEQ: VARS, Y-VARS, enter, enter, enter, enter)
2. To show the residual plot:
StatPlot (2nd, y=)
Open Statplot #1, 'ON'
YList: RESID (2nd, Stat, RESID)
3. Clear the 'y=' function for the line of best fit (seeing the line appear with the residual plot is confusing).
4. Zoom, #9 to show the Residual Plot.
What do you see?
Does this mean the linear model equation is appropriate for making predictions?

Yes, the linear model is appropriate.

No, the linear model is not appropriate.

Random scatter.

Definite pattern or curve.

4

Look back at the table for today's activity, or use Stat Edit. There are two children that have unusual results.
Look at child #18, who has unusual results.
Use the Age at First Word for this child and find their predicted Gesell Score.
Enter it below to two places past the decimal.

4

Using the information from #8, find the residual for Child #18.
Enter it below to two places past the decimal.

4

Look back at the table for today's activity, or use Stat Edit. There are two children that have unusual results.
NOW, look at child #19, who also has unusual results.
Use the Age at First Word for this child and find their predicted Gesell Score.
Enter it below to two places past the decimal.

4

Using the information from #10, find the residual for Child #19.
Enter it below to two places past the decimal.

4

Based on looking at the data table (note the age and Gesell scores) and looking at the residuals, why are both children considered outliers?
Match their number with the correct reason.

Stavka koja se može prevući		Odgovarajuća stavka
Child #19		The x value(age at first word) is far from the rest of the data values, but making it an outlier even though the residual is not large.
		The actual data point (age at first word, Gesell Score) puts it far away from the main group of the data, making it an outlier with a large residual.
Child #18		The type of outlier and reason cannot be determined with the information provided.

4

Using the data lists in L1 and L2, let's observe the influence of each of the unusual points.
Start with Child #18 (42, 57).
Remember the original data gave the correlation coefficient: -0.640
slope: -1.127 pts/month
y-intercept: 109.874 points
1. Go into L1 and L2, REMOVE the data for child #18 (use 'del')
2. Redo the Linear Regression (stat, calc, #8) WITHOUT the data for child #18.
3. Match the information to the new numbers.

Stavka koja se može prevući		Odgovarajuća stavka
Intercept		-0.335
Original Intercept		-0.779
Original Slope		105.63
Correlation Coefficient		109.874
Slope		-1.127

4

NOW add back the data for child #18, it is ok to just add (42, 57) at the end of L1 and L2.
Using the data lists in L1 and L2, let's observe the influence of the unusual point for child #19 (17, 121).
Remember the original data gave the correlation coefficient: -0.640
slope: -1.127 pts/month
y-intercept: 109.874 points
1. Go into L1 and L2, REMOVE the data for child #19.
2. Redo the Linear Regression (stat, calc, #8) WITHOUT the data for child #19.
3. Match the information to the new numbers.

Stavka koja se može prevući		Odgovarajuća stavka
Intercept		-0.756
Original Intercept		-1.193
Original Slope		109.305
Correlation Coefficient		109.874
Slope		-1.127

4

Now we will compare Child #18 and Child #19.
Remember: an observation that is influential for a statistical calculation will cause a marked change in the intercept, slope and correlation coefficient when it is REMOVED.
Which of the two points is considered an INFLUENTIAL point?
Why?
Choose both correct answers below.

It is influential because it does not change the correlation coefficient, slope and intercept the most when it is removed.

The data for Child #18 is an influential point.

It is influential because it changes the correlation coefficient, slope and intercept the most when it is removed.

The data for Child #19 is an influential point.

It is influential because it only changes the correlation coefficient, slope and intercept slightly when it is removed.

Day 10 Influential Points Activity

With the data in L1 and L2, create a scatterplot showing the relationship between age and Gesell Score.Use Statplot (2nd, y=).Describe the relationship between age at first word and Gesell Score:Select all answers that apply.

Do a linear regression (Stat, Calc, #8) to calculate the correlation coefficient.Enter the value rounded to three places past the decimal point.Be careful to note the sign.

Use the linear regression information to create a Linear Model Equation for predicting Gesell Score based on Age at First Word.Match the numbers and variables with the correct description.

Explain the meaning of the slope in this context.Correct the answer below:

Explain the meaning of the intercept in this context.Correct the answer below:

Look back at the table for today's activity, or use Stat Edit. There are two children that have unusual results.Look at child #18, who has unusual results.Use the Age at First Word for this child and find their predicted Gesell Score.Enter it below to two places past the decimal.

Using the information from #8, find the residual for Child #18.Enter it below to two places past the decimal.

Look back at the table for today's activity, or use Stat Edit. There are two children that have unusual results.NOW, look at child #19, who also has unusual results.Use the Age at First Word for this child and find their predicted Gesell Score.Enter it below to two places past the decimal.

Using the information from #10, find the residual for Child #19.Enter it below to two places past the decimal.

Based on looking at the data table (note the age and Gesell scores) and looking at the residuals, why are both children considered outliers?Match their number with the correct reason.

With the data in L1 and L2, create a scatterplot showing the relationship between age and Gesell Score.Use Statplot (2nd, y=).Describe the relationship between age at first word and Gesell Score:Select all answers that apply.

Do a linear regression (Stat, Calc, #8) to calculate the correlation coefficient.Enter the value rounded to three places past the decimal point.Be careful to note the sign.

Use the linear regression information to create a Linear Model Equation for predicting Gesell Score based on Age at First Word.Match the numbers and variables with the correct description.

Explain the meaning of the slope in this context.Correct the answer below:

Explain the meaning of the intercept in this context.Correct the answer below:

Look back at the table for today's activity, or use Stat Edit. There are two children that have unusual results.Look at child #18, who has unusual results.Use the Age at First Word for this child and find their predicted Gesell Score.Enter it below to two places past the decimal.

Using the information from #8, find the residual for Child #18.Enter it below to two places past the decimal.

Look back at the table for today's activity, or use Stat Edit. There are two children that have unusual results.NOW, look at child #19, who also has unusual results.Use the Age at First Word for this child and find their predicted Gesell Score.Enter it below to two places past the decimal.

Using the information from #10, find the residual for Child #19.Enter it below to two places past the decimal.

Based on looking at the data table (note the age and Gesell scores) and looking at the residuals, why are both children considered outliers?Match their number with the correct reason.

With the data in L1 and L2, create a scatterplot showing the relationship between age and Gesell Score.
Use Statplot (2nd, y=).
Describe the relationship between age at first word and Gesell Score:
Select all answers that apply.

Do a linear regression (Stat, Calc, #8) to calculate the correlation coefficient.
Enter the value rounded to three places past the decimal point.
Be careful to note the sign.

Use the linear regression information to create a Linear Model Equation for predicting Gesell Score based on Age at First Word.
Match the numbers and variables with the correct description.

Explain the meaning of the slope in this context.
Correct the answer below:

Explain the meaning of the intercept in this context.
Correct the answer below:

Look back at the table for today's activity, or use Stat Edit. There are two children that have unusual results.
Look at child #18, who has unusual results.
Use the Age at First Word for this child and find their predicted Gesell Score.
Enter it below to two places past the decimal.

Using the information from #8, find the residual for Child #18.
Enter it below to two places past the decimal.

Look back at the table for today's activity, or use Stat Edit. There are two children that have unusual results.
NOW, look at child #19, who also has unusual results.
Use the Age at First Word for this child and find their predicted Gesell Score.
Enter it below to two places past the decimal.

Using the information from #10, find the residual for Child #19.
Enter it below to two places past the decimal.

Based on looking at the data table (note the age and Gesell scores) and looking at the residuals, why are both children considered outliers?
Match their number with the correct reason.

With the data in L1 and L2, create a scatterplot showing the relationship between age and Gesell Score.
Use Statplot (2nd, y=).
Describe the relationship between age at first word and Gesell Score:
Select all answers that apply.

Do a linear regression (Stat, Calc, #8) to calculate the correlation coefficient.
Enter the value rounded to three places past the decimal point.
Be careful to note the sign.

Use the linear regression information to create a Linear Model Equation for predicting Gesell Score based on Age at First Word.
Match the numbers and variables with the correct description.

Explain the meaning of the slope in this context.
Correct the answer below:

Explain the meaning of the intercept in this context.
Correct the answer below:

Look back at the table for today's activity, or use Stat Edit. There are two children that have unusual results.
Look at child #18, who has unusual results.
Use the Age at First Word for this child and find their predicted Gesell Score.
Enter it below to two places past the decimal.

Using the information from #8, find the residual for Child #18.
Enter it below to two places past the decimal.

Look back at the table for today's activity, or use Stat Edit. There are two children that have unusual results.
NOW, look at child #19, who also has unusual results.
Use the Age at First Word for this child and find their predicted Gesell Score.
Enter it below to two places past the decimal.

Using the information from #10, find the residual for Child #19.
Enter it below to two places past the decimal.

Based on looking at the data table (note the age and Gesell scores) and looking at the residuals, why are both children considered outliers?
Match their number with the correct reason.