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lines changed Original file line number Diff line number Diff line change @@ -28,13 +28,13 @@ Bartlett's test is used to test the null hypothesis that the variances of k grou
2828
2929For ` k ` groups each with ` n_i ` observations, the test statistic is
3030
31- <!-- <equation class="equation" label="eq:bartlett-test-statistic" align="center" raw="\chi^2 = \frac{N\ln(S^2) - \sum_{i=0}^{k-1} n_i \ln(S_i^2)}{1 + \frac{1}{3(k-1)}\left(\sum_{i=0}^{k-1} \frac{1}{n_i} - \frac{1}{N}\right)}" alt="Equation for Bartlett's test statistic."> -->
31+ <!-- <equation class="equation" label="eq:bartlett-test-statistic" align="center" raw="\chi^2 = \frac{\displaystyle N\ln(S^2) - \sum_{i=0}^{k-1} n_i \ln(S_i^2)}{\displaystyle 1 + \frac{1}{3(k-1)}\left(\sum_{i=0}^{k-1} \frac{1}{n_i} - \frac{1}{N}\right)}" alt="Equation for Bartlett's test statistic."> -->
3232
3333``` math
34- \chi^2 = \frac{N\ln(S^2) - \sum_{i=0}^{k-1} n_i \ln(S_i^2)}{1 + \frac{1}{3(k-1)}\left(\sum_{i=0}^{k-1} \frac{1}{n_i} - \frac{1}{N}\right)}
34+ \chi^2 = \frac{\displaystyle N\ln(S^2) - \sum_{i=0}^{k-1} n_i \ln(S_i^2)}{\displaystyle 1 + \frac{1}{3(k-1)}\left(\sum_{i=0}^{k-1} \frac{1}{n_i} - \frac{1}{N}\right)}
3535```
3636
37- <!-- <div class="equation" align="center" data-raw-text="\chi^2 = \frac{N\ln(S^2) - \sum_{i=0}^{k-1} n_i \ln(S_i^2)}{1 + \frac{1}{3(k-1)}\left(\sum_{i=0}^{k-1} \frac{1}{n_i} - \frac{1}{N}\right)}" data-equation="eq:bartlett-test-statistic">
37+ <!-- <div class="equation" align="center" data-raw-text="\chi^2 = \frac{\displaystyle N\ln(S^2) - \sum_{i=0}^{k-1} n_i \ln(S_i^2)}{\displaystyle 1 + \frac{1}{3(k-1)}\left(\sum_{i=0}^{k-1} \frac{1}{n_i} - \frac{1}{N}\right)}" data-equation="eq:bartlett-test-statistic">
3838 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@4b1db4ebd815eb54bf53a3fa132b992604743d9c/lib/node_modules/@stdlib/stats/bartlett-test/docs/img/equation_bartlett-test-statistic.svg" alt="Equation for Bartlett's test statistic.">
3939 <br>
4040</div> -->
Original file line number Diff line number Diff line change @@ -43,13 +43,13 @@ where the numerator is the [covariance][covariance] and the denominator is the p
4343
4444For a sample of size ` n ` , the sample [ Pearson product-moment correlation coefficient] [ pearson-correlation ] is defined as
4545
46- <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
46+ <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
4747
4848``` math
49- r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
49+ r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
5050```
5151
52- <!-- <div class="equation" align="center" data-raw-text="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
52+ <!-- <div class="equation" align="center" data-raw-text="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
5353 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@80f96253bf726f33bc71d8eb68037ab203ae4cf9/lib/node_modules/@stdlib/stats/incr/apcorr/docs/img/equation_sample_pearson_correlation_coefficient.svg" alt="Equation for the sample Pearson product-moment correlation coefficient.">
5454 <br>
5555</div> -->
Original file line number Diff line number Diff line change @@ -26,13 +26,13 @@ limitations under the License.
2626
2727The [ harmonic mean] [ harmonic-mean ] of positive real numbers ` x_0, x_1, ..., x_{n-1} ` is defined as
2828
29- <!-- <equation class="equation" label="eq:harmonic_mean" align="center" raw="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}" alt="Equation for the harmonic mean."> -->
29+ <!-- <equation class="equation" label="eq:harmonic_mean" align="center" raw="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{\displaystyle n}{\displaystyle\ sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\displaystyle\ sum_{i=0}^{n-1} \frac{1}{x_i}}{\displaystyle n} \biggr)^{-1}\end{align}" alt="Equation for the harmonic mean."> -->
3030
3131``` math
32- \begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}
32+ \begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{\displaystyle n}{\displaystyle\ sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\displaystyle\ sum_{i=0}^{n-1} \frac{1}{x_i}}{\displaystyle n} \biggr)^{-1}\end{align}
3333```
3434
35- <!-- <div class="equation" align="center" data-raw-text="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}" data-equation="eq:harmonic_mean">
35+ <!-- <div class="equation" align="center" data-raw-text="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{\displaystyle n}{\displaystyle\ sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\displaystyle\ sum_{i=0}^{n-1} \frac{1}{x_i}}{\displaystyle n} \biggr)^{-1}\end{align}" data-equation="eq:harmonic_mean">
3636 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@2b632747053b9e357a4663369528fe62b29a6d55/lib/node_modules/@stdlib/stats/incr/hmean/docs/img/equation_harmonic_mean.svg" alt="Equation for the harmonic mean.">
3737 <br>
3838</div> -->
Original file line number Diff line number Diff line change @@ -60,13 +60,13 @@ where `m_4` is the sample fourth central moment and `m_2` is the sample second c
6060
6161The previous equation is, however, a biased estimator of the population excess kurtosis. An alternative estimator which is unbiased under normality is
6262
63- <!-- <equation class="equation" label="eq:corrected_sample_excess_kurtosis" align="center" raw="G_2 = \frac{(n+1)n}{(n-1)(n-2)(n-3)} \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2} - 3 \frac{(n-1)^2}{(n-2)(n-3)}" alt="Equation for the corrected sample excess kurtosis."> -->
63+ <!-- <equation class="equation" label="eq:corrected_sample_excess_kurtosis" align="center" raw="G_2 = \frac{(n+1)n}{(n-1)(n-2)(n-3)} \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2} - 3 \frac{(n-1)^2}{(n-2)(n-3)}" alt="Equation for the corrected sample excess kurtosis."> -->
6464
6565``` math
66- G_2 = \frac{(n+1)n}{(n-1)(n-2)(n-3)} \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2} - 3 \frac{(n-1)^2}{(n-2)(n-3)}
66+ G_2 = \frac{(n+1)n}{(n-1)(n-2)(n-3)} \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2} - 3 \frac{(n-1)^2}{(n-2)(n-3)}
6767```
6868
69- <!-- <div class="equation" align="center" data-raw-text="G_2 = \frac{(n+1)n}{(n-1)(n-2)(n-3)} \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2} - 3 \frac{(n-1)^2}{(n-2)(n-3)}" data-equation="eq:corrected_sample_excess_kurtosis">
69+ <!-- <div class="equation" align="center" data-raw-text="G_2 = \frac{(n+1)n}{(n-1)(n-2)(n-3)} \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})^4}{\biggl(\sum_{i=0}^{n-1} (x_i - \bar{x})^2\biggr)^2} - 3 \frac{(n-1)^2}{(n-2)(n-3)}" data-equation="eq:corrected_sample_excess_kurtosis">
7070 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/kurtosis/docs/img/equation_corrected_sample_excess_kurtosis.svg" alt="Equation for the corrected sample excess kurtosis.">
7171 <br>
7272</div> -->
Original file line number Diff line number Diff line change @@ -26,13 +26,13 @@ limitations under the License.
2626
2727The [ mean absolute error] [ mean-absolute-error ] is defined as
2828
29- <!-- <equation class="equation" label="eq:mean_absolute_error" align="center" raw="\operatorname{MAE} = \frac{\sum_{i=0}^{n-1} |y_i - x_i|}{n}" alt="Equation for the mean absolute error."> -->
29+ <!-- <equation class="equation" label="eq:mean_absolute_error" align="center" raw="\operatorname{MAE} = \frac{\displaystyle\ sum_{i=0}^{n-1} |y_i - x_i|}{n}" alt="Equation for the mean absolute error."> -->
3030
3131``` math
32- \operatorname{MAE} = \frac{\sum_{i=0}^{n-1} |y_i - x_i|}{n}
32+ \operatorname{MAE} = \frac{\displaystyle\ sum_{i=0}^{n-1} |y_i - x_i|}{n}
3333```
3434
35- <!-- <div class="equation" align="center" data-raw-text="\operatorname{MAE} = \frac{\sum_{i=0}^{n-1} |y_i - x_i|}{n}" data-equation="eq:mean_absolute_error">
35+ <!-- <div class="equation" align="center" data-raw-text="\operatorname{MAE} = \frac{\displaystyle\ sum_{i=0}^{n-1} |y_i - x_i|}{n}" data-equation="eq:mean_absolute_error">
3636 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/mae/docs/img/equation_mean_absolute_error.svg" alt="Equation for the mean absolute error.">
3737 <br>
3838</div> -->
Original file line number Diff line number Diff line change @@ -43,13 +43,13 @@ where the numerator is the [covariance][covariance] and the denominator is the p
4343
4444For a sample of size ` W ` , the sample [ Pearson product-moment correlation coefficient] [ pearson-correlation ] is defined as
4545
46- <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
46+ <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
4747
4848``` math
49- r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
49+ r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
5050```
5151
52- <!-- <div class="equation" align="center" data-raw-text="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
52+ <!-- <div class="equation" align="center" data-raw-text="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
5353 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@e7c0cbc398c5e64614baf47cf5c6259b93c0ffce/lib/node_modules/@stdlib/stats/incr/mapcorr/docs/img/equation_sample_pearson_correlation_coefficient.svg" alt="Equation for the sample Pearson product-moment correlation coefficient.">
5454 <br>
5555</div> -->
Original file line number Diff line number Diff line change @@ -26,13 +26,13 @@ limitations under the License.
2626
2727The [ harmonic mean] [ harmonic-mean ] of positive real numbers ` x_0, x_1, ..., x_{n-1} ` is defined as
2828
29- <!-- <equation class="equation" label="eq:harmonic_mean" align="center" raw="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}" alt="Equation for the harmonic mean."> -->
29+ <!-- <equation class="equation" label="eq:harmonic_mean" align="center" raw="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\displaystyle\ sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}" alt="Equation for the harmonic mean."> -->
3030
3131``` math
32- \begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}
32+ \begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\displaystyle\ sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}
3333```
3434
35- <!-- <div class="equation" align="center" data-raw-text="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}" data-equation="eq:harmonic_mean">
35+ <!-- <div class="equation" align="center" data-raw-text="\begin{align}H &= \frac{n}{\frac{1}{x_0} + \frac{1}{x_1} + \cdots + \frac{1}{x_{n-1}}} \\ &= \frac{n}{\sum_{i=0}^{n-1} \frac{1}{x_i}} \\ &= \biggl( \frac{\displaystyle \ sum_{i=0}^{n-1} \frac{1}{x_i}}{n} \biggr)^{-1}\end{align}" data-equation="eq:harmonic_mean">
3636 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@0a561712608b99b59d9243f7d478a2e2a019a130/lib/node_modules/@stdlib/stats/incr/mhmean/docs/img/equation_harmonic_mean.svg" alt="Equation for the harmonic mean.">
3737 <br>
3838</div> -->
Original file line number Diff line number Diff line change @@ -43,10 +43,10 @@ where the numerator is the [covariance][covariance] and the denominator is the p
4343
4444For a sample of size ` W ` , the [ sample Pearson product-moment correlation coefficient] [ pearson-correlation ] is defined as
4545
46- <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
46+ <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
4747
4848``` math
49- r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
49+ r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
5050```
5151
5252<!-- <div class="equation" align="center" data-raw-text="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
Original file line number Diff line number Diff line change @@ -43,13 +43,13 @@ where the numerator is the [covariance][covariance] and the denominator is the p
4343
4444For a sample of size ` n ` , the [ sample Pearson product-moment correlation coefficient] [ pearson-correlation ] is defined as
4545
46- <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
46+ <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
4747
4848``` math
49- r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
49+ r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
5050```
5151
52- <!-- <div class="equation" align="center" data-raw-text="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
52+ <!-- <div class="equation" align="center" data-raw-text="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
5353 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@49d8cabda84033d55d7b8069f19ee3dd8b8d1496/lib/node_modules/@stdlib/stats/incr/pcorr/docs/img/equation_sample_pearson_correlation_coefficient.svg" alt="Equation for the sample Pearson product-moment correlation coefficient.">
5454 <br>
5555</div> -->
Original file line number Diff line number Diff line change @@ -43,13 +43,13 @@ where the numerator is the [covariance][covariance] and the denominator is the p
4343
4444For a sample of size ` n ` , the sample [ Pearson product-moment correlation coefficient] [ pearson-correlation ] is defined as
4545
46- <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
46+ <!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->
4747
4848``` math
49- r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
49+ r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}
5050```
5151
52- <!-- <div class="equation" align="center" data-raw-text="r = \frac{\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
52+ <!-- <div class="equation" align="center" data-raw-text="r = \frac{\displaystyle\ sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle \sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
5353 <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@0086d9dadd17859fedeb3c5acc3a80d7011970e1/lib/node_modules/@stdlib/stats/incr/pcorr2/docs/img/equation_sample_pearson_correlation_coefficient.svg" alt="Equation for the sample Pearson product-moment correlation coefficient.">
5454 <br>
5555</div> -->
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