Correlation Study In Statistical Analysis

Explanation
Sir Francis Galton is credited with discovering correlation analysis. He was a British scientist and cousin of Charles Darwin. Galton developed the concept of correlation to measure the relationship between two variables. He conducted extensive research on heredity and statistical analysis, and his work laid the foundation for modern correlation analysis. Galton's contributions to the field of statistics and his development of correlation analysis have had a lasting impact on various scientific disciplines.

Explanation
Temporal precedence refers to the principle that the presumed cause must occur before the presumed effect. In other words, there should be a clear temporal order between the cause and the effect. This principle is important in establishing causal relationships and determining the directionality of the relationship between variables. Without temporal precedence, it would be difficult to determine whether a particular event or factor is truly causing an effect or if it is the other way around.

Explanation
The range of the Correlation Coefficient is +1.00 to -1.00. This means that the correlation coefficient can take values between +1.00 and -1.00, inclusive. A correlation coefficient of +1.00 indicates a perfect positive linear relationship between two variables, while a correlation coefficient of -1.00 indicates a perfect negative linear relationship. A correlation coefficient of 0 indicates no linear relationship between the variables.

Explanation
A correlation coefficient of 0.5 suggests that there is a moderate positive linear relationship between the x and y variables in the dataset. This means that as the x variable increases, the y variable also tends to increase, but not necessarily at a 1:1 ratio.

Explanation
A scatter plot is a graph that represents relationships between two variables using ordered pairs (x, y). It allows us to visually analyze the relationship between the variables and determine if any patterns or trends exist. Therefore, the correct answer is Scatter Plots.

Explanation
The coefficient of determination (R-squared) is a measure of how well the regression model fits the observed data. It represents the proportion of the variance in the dependent variable that can be explained by the independent variable(s). The correlation coefficient (r) measures the strength and direction of the linear relationship between two variables. The square root of the coefficient of determination is equal to the absolute value of the correlation coefficient. Therefore, if the coefficient of determination is 0.64, the correlation coefficient can be either 0.80 or -0.80.

Explanation
Pearson's r, also known as Pearson's correlation coefficient, measures the strength and direction of the linear relationship between two continuous variables. It ranges from -1 to +1, where -1 indicates a perfect negative linear relationship, +1 indicates a perfect positive linear relationship, and 0 indicates no linear relationship. Therefore, Pearson's r is used to determine the standard of the linear relationship between variables.

Explanation
Type II error is the correct answer. This error occurs when the null hypothesis is incorrectly accepted, meaning that the researcher fails to reject the null hypothesis even though it is actually false. In other words, it is a false negative result, where the researcher concludes that there is no effect or relationship when there actually is. This error is often associated with a lack of statistical power or a small sample size, which increases the likelihood of failing to detect a true effect.

Explanation
The value of One-tailed p is 0.025. This value represents the significance level or the probability of obtaining a test statistic as extreme as the one observed, assuming the null hypothesis is true. In hypothesis testing, a significance level of 0.025 indicates a 2.5% chance of observing such extreme results by chance alone, leading to the rejection of the null hypothesis.

Explanation
The null hypothesis is the other name for the statistical hypothesis. It is a statement that assumes there is no significant difference or relationship between variables in a population. It is used in hypothesis testing to determine if the alternative hypothesis can be accepted or rejected based on the evidence from the sample data. Power analysis refers to the calculation of statistical power, while product-moment correlation is a statistical measure of the strength and direction of the linear relationship between two variables. Therefore, neither power analysis nor product-moment correlation are alternative names for the statistical hypothesis.