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The dataset available on Study Direct contains annual sales data and other characteristics of 400 Dutch fashion stores in 1990. The following variables appear in the data set: - Essay Example

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This assignment uses a sample dataset containing five variables; each of them presents the results of 400 observations. The data set…
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The dataset available on Study Direct contains annual sales data and other characteristics of 400 Dutch fashion stores in 1990. The following variables appear in the data set:
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"The dataset available on Study Direct contains annual sales data and other characteristics of 400 Dutch fashion stores in 1990. The following variables appear in the data set:"

Download file to see previous pages As per direction, the two variables can move in the same or opposite direction. When the variables move in the same direction, it is said that two variables have a positive direction otherwise, they have negative direction. As per strength, both variables can move in either direction together or one can lag behind the other. The domain of the direction is (-1, +1). The pairwise correlation coefficient is denoted by the letter “r”; it defines the following (PENN STATE n.d.):
The scatterplot (Stat Trek n.d.) in Figure 1 depicts the correlation between sales as a dependent variable and hoursw as an independent variable. The relationship between the variables is positive, and not very strong. The value of “r” is evaluated using Excel formula CORREL (hoursw Array, sales Array) = 0.26. The statistical significance is tested for the null hypothesis, r = 0. The value of t-stat is calculated using the formula (Vassarstarts n.d.) t-stat = r / sqrt[(1-r^2) / (N-2). In this equation, the expression (N-2) is called the degree of freedom, df. Hence, t-stat = 0.26 / sqrt[(1-0.26^2) / (401-2) = 5.44; the value of t critical for df=399 at p = 0.05 (2-tail) is 1.9719. At the same time, r(399) = 0.26 , α = 0.001. Therefore, reject the null for t-stat > t critical and p < α. We can conclude that there is a statistically significant relationship between these variables (California State University n.d.).
The scatterplot in Figure 2 shows that the correlation is positive, and not strong. The value of “r” is calculated using CORREL =( nfull Array, sales Array) = 0.24. The value of t-stat (df=399, r = 0.24)= 4.88. The value of t-critical (df = 399, p = 0.05) = 1.9719. The value of α (df = 399, r= 0.24, t = 4.88) = 0.001. For t-stat > t-critical and p < α, we reject null r = 0. Therefore, there is a statistically significant relationship between these ...Download file to see next pagesRead More
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