1
Correlation Between Bears Chest Size and Weights
Pearson's Correlations
n Pearson's r p
CHEST - WEIGHT 54 0.963 < .001
Table 1
A classical correlation test was done in Jasp to measure if there is correlation
between chest size and weights of randomly selected sample of 54 bears. The null hypothesis
for this test is there is no correlation between the bears chest size and their weights (r=0) and
the alternative hypothesis there is correlation between the bears chest size and their weights (r
≠0). Table 1 above depicts the results from this test. The Pearson’s r column is the linear
correlation coefficient, which was identified as 0.963. Based on these results, there is
sufficient evidence to suggests that the bear chest size and their weights are correlated. This is
because the linear correlation coefficient or Pearson’s r, is on a scale from -1 to 1, 0 indicates
that there is no correlation and values closer to negative one or to positive one indicates
correlation. The Pearson’s r value, 0.963 is closer to the 1 value, therefore there is positive
correlation between the bears chest size and their weights. The positive correlation means that
as the bears chest size increase, their weights also increase. The column labelled ‘p’ is the p-
value identified. This can also be used to identify if there is correlation between the two
variables. Because the P-value, 0.001, it indicates that when a 0.05, 0.1, or 0.01 significance
level is applied, it would result in the rejection of the null hypothesis because the p-value is
less than the alpha value, making it significant. The results of the Pearson’s r value, 0.963,
and the P-value, 0.001, reject the null hypothesis that there is no correlation between the
bears chest size and their weights. Therefore, there is sufficient evidence to state that there is
correlation between the bears chest size and their weights.
, 2
Scatter plot of Chest and Weight Size of Bears
CHEST vs. WEIGHT
Figure one
Figure one above, which is a scatter plot of the two variables, also supports the
notion to reject the null hypothesis. The data points are extremely close to the regression line,
and it can be seen that as chest size increases, the weight also increases indicating that there is
correlation.
Linear Regression for Chest Size and Weight
Model Summary - WEIGHT
Model R R² Adjusted R² RMSE
H₁ 0.963 0.928 0.926 33.078
Table 2
The important concepts in Table 2 above are labelled as ‘R’, ‘R2’, and ‘Adjusted R2’
in the columns. The R, 0.963, is the linear correlation coefficient and was already explained
previously. The R2 is the coefficient of determination and is used to represent how well the
data are fitted to the regression line. The R2 value is 0.928, indicates that the data do in fact
represents the data well as most are extremely close to the regression line, making it a good
fit. This indicated that 92.8% of the weight variation can be explained by chest size. The
adjusted R2 value, 0.926, also indicated what proportion of the dependent variable (weight),
Correlation Between Bears Chest Size and Weights
Pearson's Correlations
n Pearson's r p
CHEST - WEIGHT 54 0.963 < .001
Table 1
A classical correlation test was done in Jasp to measure if there is correlation
between chest size and weights of randomly selected sample of 54 bears. The null hypothesis
for this test is there is no correlation between the bears chest size and their weights (r=0) and
the alternative hypothesis there is correlation between the bears chest size and their weights (r
≠0). Table 1 above depicts the results from this test. The Pearson’s r column is the linear
correlation coefficient, which was identified as 0.963. Based on these results, there is
sufficient evidence to suggests that the bear chest size and their weights are correlated. This is
because the linear correlation coefficient or Pearson’s r, is on a scale from -1 to 1, 0 indicates
that there is no correlation and values closer to negative one or to positive one indicates
correlation. The Pearson’s r value, 0.963 is closer to the 1 value, therefore there is positive
correlation between the bears chest size and their weights. The positive correlation means that
as the bears chest size increase, their weights also increase. The column labelled ‘p’ is the p-
value identified. This can also be used to identify if there is correlation between the two
variables. Because the P-value, 0.001, it indicates that when a 0.05, 0.1, or 0.01 significance
level is applied, it would result in the rejection of the null hypothesis because the p-value is
less than the alpha value, making it significant. The results of the Pearson’s r value, 0.963,
and the P-value, 0.001, reject the null hypothesis that there is no correlation between the
bears chest size and their weights. Therefore, there is sufficient evidence to state that there is
correlation between the bears chest size and their weights.
, 2
Scatter plot of Chest and Weight Size of Bears
CHEST vs. WEIGHT
Figure one
Figure one above, which is a scatter plot of the two variables, also supports the
notion to reject the null hypothesis. The data points are extremely close to the regression line,
and it can be seen that as chest size increases, the weight also increases indicating that there is
correlation.
Linear Regression for Chest Size and Weight
Model Summary - WEIGHT
Model R R² Adjusted R² RMSE
H₁ 0.963 0.928 0.926 33.078
Table 2
The important concepts in Table 2 above are labelled as ‘R’, ‘R2’, and ‘Adjusted R2’
in the columns. The R, 0.963, is the linear correlation coefficient and was already explained
previously. The R2 is the coefficient of determination and is used to represent how well the
data are fitted to the regression line. The R2 value is 0.928, indicates that the data do in fact
represents the data well as most are extremely close to the regression line, making it a good
fit. This indicated that 92.8% of the weight variation can be explained by chest size. The
adjusted R2 value, 0.926, also indicated what proportion of the dependent variable (weight),
