Math / Data & Statistics

Question12.1 HW Question 5, 10.1.9 HW Score: $6.9 \%, 2$ of 29 points Part 2 of 6 Points: 0 of 1 Save
Refer to the accompanying scatterplot. a. Examine the pattern of all 10 points and subjectively determine whether there appears to be a strong correlation between $x$ and $y$ . $\mathbf{b}$ . Find the value of the correlation coefficient $r$ and determine whether there is a linear correlation. $\mathbf{c}$ . Remove the point with coordinates $10-$ $(10,2)$ and find the correlation coefficient r and determine whether there is a linear correlation. d . What do you conclude about the possible effect from a single pair of values? Click here to view a table of critical values for the correlation coefficient. a. Do the data points appear to have a strong linear correlation? No Yes b. What is the value of the correlation coefficient for all 10 data points? $\mathrm{r}=$ $\square$ (Simplify your answer. Round to three decimal places as needed.)
Table of Critical Values $\square$ \begin{tabular}{|c|c|c|} \hline n & $\alpha=.05$ & $\alpha=.01$ \\ \hline 4 & . 950 & . 990 \\ \hline 5 & . 878 & . 959 \\ \hline 6 & . 811 & . 917 \\ \hline 7 & . 754 & .875 \\ \hline 8 & . 707 & . 834 \\ \hline 9 & . 666 & . 798 \\ \hline 10 & . 632 & . 765 \\ \hline 11 & . 602 & . 735 \\ \hline 12 & . 576 & . 708 \\ \hline 13 & . 553 & . 684 \\ \hline 14 & . 532 & . 661 \\ \hline 15 & . 514 & . 641 \\ \hline 16 & . 497 & . 623 \\ \hline 17 & . 482 & . 606 \\ \hline 18 & - . 468 & . 590 \\ \hline 19 & . 456 & .575 \\ \hline 20 & . 444 & . 561 \\ \hline 25 & . 396 & .505 \\ \hline 30 & . 361 & . 463 \\ \hline 35 & . 335 & 430 \\ \hline 40 & . 312 & . 402 \\ \hline 15 & 304 & 270 \\ \hline \end{tabular} Get more help -

Studdy Solution

STEP 1

1. We have a scatterplot with 10 data points.
2. One of the points is an outlier at (10, 2).
3. We need to determine the correlation coefficient $r$ for the data set with and without the outlier.
4. We will use the critical values table to assess the significance of the correlation.

STEP 2

1. Examine the scatterplot for a visual assessment of correlation.
2. Calculate the correlation coefficient $r$ for all 10 points.
3. Determine the significance of the correlation using the critical values table.
4. Remove the outlier and recalculate the correlation coefficient $r$ .
5. Determine the significance of the new correlation.
6. Conclude the effect of the outlier on the correlation.

STEP 3

Examine the scatterplot to visually assess the correlation between $x$ and $y$ .
- Look for a pattern or trend in the data points. - Determine if the points suggest a strong linear relationship.

STEP 4

Calculate the correlation coefficient $r$ for all 10 data points.
- Use the formula for the Pearson correlation coefficient:
$r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}$
- Substitute the values from the data set into the formula.

STEP 5

Determine the significance of the correlation using the critical values table.
- Compare the calculated $r$ with the critical value for $n = 10$ at $\alpha = 0.05$ and $\alpha = 0.01$ .

STEP 6

Remove the outlier point (10, 2) and recalculate the correlation coefficient $r$ .
- Recalculate $r$ using the remaining 9 data points.

STEP 7

Determine the significance of the new correlation.
- Compare the new $r$ with the critical value for $n = 9$ at $\alpha = 0.05$ and $\alpha = 0.01$ .

STEP 8

Conclude the effect of the outlier on the correlation.
- Discuss how the outlier affects the strength and significance of the correlation.
The solution involves calculating the correlation coefficients and comparing them with critical values to assess the impact of the outlier on the correlation.

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Studdy Solution

STEP 1

1. We have a scatterplot with 10 data points.
2. One of the points is an outlier at (10, 2).
3. We need to determine the correlation coefficient $r$ for the data set with and without the outlier.
4. We will use the critical values table to assess the significance of the correlation.

STEP 2

STEP 3

Examine the scatterplot to visually assess the correlation between $x$ and $y$ .
- Look for a pattern or trend in the data points. - Determine if the points suggest a strong linear relationship.

STEP 4

Calculate the correlation coefficient $r$ for all 10 data points.
- Use the formula for the Pearson correlation coefficient:
$r = \frac{n(\sum xy) - (\sum x)(\sum y)}{\sqrt{[n\sum x^2 - (\sum x)^2][n\sum y^2 - (\sum y)^2]}}$
- Substitute the values from the data set into the formula.

STEP 5

Determine the significance of the correlation using the critical values table.
- Compare the calculated $r$ with the critical value for $n = 10$ at $\alpha = 0.05$ and $\alpha = 0.01$ .

STEP 6

Remove the outlier point (10, 2) and recalculate the correlation coefficient $r$ .
- Recalculate $r$ using the remaining 9 data points.

STEP 7

Determine the significance of the new correlation.
- Compare the new $r$ with the critical value for $n = 9$ at $\alpha = 0.05$ and $\alpha = 0.01$ .

STEP 8

Conclude the effect of the outlier on the correlation.
- Discuss how the outlier affects the strength and significance of the correlation.
The solution involves calculating the correlation coefficients and comparing them with critical values to assess the impact of the outlier on the correlation.

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Studdy Solution

STEP 1

1. We have a scatterplot with 10 data points.2. One of the points is an outlier at (10, 2).3. We need to determine the correlation coefficient r r r for the data set with and without the outlier.4. We will use the critical values table to assess the significance of the correlation.

STEP 2

STEP 3

Examine the scatterplot to visually assess the correlation between x x x and y y y.- Look for a pattern or trend in the data points. - Determine if the points suggest a strong linear relationship.

STEP 4

STEP 5

Determine the significance of the correlation using the critical values table.- Compare the calculated r r r with the critical value for n=10 n = 10 n=10 at α=0.05\alpha = 0.05α=0.05 and α=0.01\alpha = 0.01α=0.01.

STEP 6

Remove the outlier point (10, 2) and recalculate the correlation coefficient r r r.- Recalculate r r r using the remaining 9 data points.

STEP 7

Determine the significance of the new correlation.- Compare the new r r r with the critical value for n=9 n = 9 n=9 at α=0.05\alpha = 0.05α=0.05 and α=0.01\alpha = 0.01α=0.01.

STEP 8

Conclude the effect of the outlier on the correlation.- Discuss how the outlier affects the strength and significance of the correlation. The solution involves calculating the correlation coefficients and comparing them with critical values to assess the impact of the outlier on the correlation.

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Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

1. We have a scatterplot with 10 data points.
2. One of the points is an outlier at (10, 2).
3. We need to determine the correlation coefficient $r$ for the data set with and without the outlier.
4. We will use the critical values table to assess the significance of the correlation.

Examine the scatterplot to visually assess the correlation between $x$ and $y$ .
- Look for a pattern or trend in the data points. - Determine if the points suggest a strong linear relationship.

Determine the significance of the correlation using the critical values table.
- Compare the calculated $r$ with the critical value for $n = 10$ at $\alpha = 0.05$ and $\alpha = 0.01$ .

Remove the outlier point (10, 2) and recalculate the correlation coefficient $r$ .
- Recalculate $r$ using the remaining 9 data points.

Determine the significance of the new correlation.
- Compare the new $r$ with the critical value for $n = 9$ at $\alpha = 0.05$ and $\alpha = 0.01$ .

Conclude the effect of the outlier on the correlation.
- Discuss how the outlier affects the strength and significance of the correlation.
The solution involves calculating the correlation coefficients and comparing them with critical values to assess the impact of the outlier on the correlation.