Q.4.159 - Elementary Statistics

Question

 High and Low Temperature. The data from Exercise 4.75 for average high and low temperatures in January for a random sample of $50$cities are on the WeissStats site.

a. decide whether use of the linear correlation coefficient as a descriptive measure for the data is appropriate. If so, then also do parts (b) and (c).

b. obtain the linear correlation coefficient.

c. interpret the value of $r$ in terms of the linear relationship between the  variables in question.

Step-by-Step Solution

Answer

a). We utilized the linear correlation coefficient as a data descriptive metric.

b). The linear correlation coefficient $=0.976$.

c).  Low and high temperatures have a significant positive relationship, according to the positive linear correlation coefficient.

Part (a) Step 1: Given Information

The table of data of average high and low temperatures in January for a random sample of $50$ cities.

Part (a) Step 2: Explanation

Draw a scatter plot for a random selection of $50$ cities' average high and low temperatures in January.

According to the scatter plot, the data points are distributed linearly.

As a consequence, as a data descriptive metric, we picked the linear correlation coefficient.

Part (b) Step 1: Given Information

High and Low Temperature. The data from Exercise 4.75 for average high and low temperatures in January for a random sample of $50$ cities are on the WeissStats site.

Part (b) Step 2: Explanation

Any technique may be used to find the correlation coefficient.

We'll begin by inputting the brides and their scores, followed by the ultimate outcome.

Hence,

The linear correlation coefficient $=0.976$.

Part (c) Step 1: Given Information

The table of data of average high and low temperatures in January for a random sample of $50$ cities.

Part (c) Step 2: Explanation

The linear correlation co-efficient $r=0.976$.

The positive linear correlation coefficient indicates a significant positive relationship between the variables low and high temperatures.