Question

the accompanying table contains data on the number of individuals with broadband access and gross domestic product (gdp) for 32 nations. let x represent gdp (in billions of u.s. dollars) and y = number of broadband users in (millions). complete parts a through e below. click the icon to view the table. a. the graph on the right shows a scatter - plot. describe this plot in terms of the association between bro a. for countries with gdp more than $5000 billion, there is a clear trend in that countries with large b. for countries with gdp less than $5000 billion, there is a clear trend in that countries with larger c. for countries with gdp less than $5000 billion, there is a clear trend in that countries with larger d. for countries with gdp more than $5000 billion, there is a clear trend in that countries with large b. give the approximate x - and y - coordinates for the nation that has the highest number of broadband s (8278,176159233) (type an ordered pair. round the x - coordinate to the nearest thousand and the y - coordinate to the near c. use software to calculate the correlation coefficient between the two variables r = (round to two decimal places as needed )

Explanation:

Step1: Recall correlation - coefficient formula

The formula for the correlation coefficient $r$ between two variables $x$ and $y$ is $r=\frac{n\sum xy-\sum x\sum y}{\sqrt{[n\sum x^{2}-(\sum x)^{2}][n\sum y^{2}-(\sum y)^{2}]}}$, where $n$ is the number of data - points.

Step2: Calculate sums from the table

First, calculate $\sum x$, $\sum y$, $\sum xy$, $\sum x^{2}$, $\sum y^{2}$ for the 32 - nation data. Let $x_i$ be the GDP and $y_i$ be the number of broadband subscribers for the $i$ - th nation.
$n = 32$.
After calculating the sums (using a statistical software or a calculator with statistical functions, for example, in Excel:

• Enter the $x$ - values (GDP) in one column and $y$ - values (broadband subscribers) in another column.
• Use functions like SUM, SUMPRODUCT, SUMSQ to calculate $\sum x$, $\sum y$, $\sum xy$, $\sum x^{2}$, $\sum y^{2}$ respectively.

Suppose $\sum x = \sum_{i = 1}^{32}x_i$, $\sum y=\sum_{i = 1}^{32}y_i$, $\sum xy=\sum_{i = 1}^{32}x_iy_i$, $\sum x^{2}=\sum_{i = 1}^{32}x_{i}^{2}$, $\sum y^{2}=\sum_{i = 1}^{32}y_{i}^{2}$.

Step3: Substitute into the formula

Substitute the values of $n$, $\sum x$, $\sum y$, $\sum xy$, $\sum x^{2}$, $\sum y^{2}$ into the correlation - coefficient formula:
$r=\frac{32\sum xy-\sum x\sum y}{\sqrt{[32\sum x^{2}-(\sum x)^{2}][32\sum y^{2}-(\sum y)^{2}]}}$.
After performing the calculations, round the result to two decimal places.

Answer:

(The actual value of $r$ depends on the calculations of the sums from the data. Without performing the actual calculations on the data in the table, we cannot give a specific numerical value. But the above steps show how to calculate it.)