Q.4.75 - Elementary Statistics

Question

High and Low Temperature, The National Oceanic and Atmospheric Administration publishes temperature information of cities around the world in Climates of the world. A random sample of 50 cities gave the data on average average high and low temperature in january shown on the Weis Stats site.

a. Obtain the scatterplot for the data

b. Decide whether finding a regression line for the data is reasonable. if so, then also do parts (c)-(f) 

c. Determine and interpret the regression equation for the data

d.Identify the potential outliers and influential observation 

e. In case a potential outlier is present, remove it and discuss the effect.

f. In case potential  influential observations is present,remove it and discuss the effect. 

Step-by-Step Solution

Answer

(a) 

b) Yes, it is reasonable for  finding a regression line. 

(c)  The regression equation for the data is $\hat{y}=-7.5692+0.9168x$

(d) There is no potential outliers and influential observation .

(e) Not applicable

(f) Not applicable 

Part(a) Step 1: Given Information

Given in the question that the National Oceanic and Atmospheric Administration publishes temperature information of cities around the world in Climates of the world. A random sample of 50 cities gave the data on average average high and low temperature in january shown on the Weis Stats site.  

we have to obtain the scatterplot for the data.  

Part(a) Step 2: Explanation

Part(b) Step 1: Given Information

Given in the question that the National Oceanic and Atmospheric Administration publishes temperature information of cities around the world in Climates of the world. A random sample of 50 cities gave the data on average average high and low temperature in january shown on the Weis Stats site.  we have to  decide whether finding a regression line for the data is reasonable  

Part(b) Step 2: Explanation

If the scatterplot has no strong curvature, it is reasonable to find the regression line for the data.

Because the scatterplot has no strong curvature, it is reasonable to identify the regression line to the data.

Part(c) Step 1: Given Information

Given in the question that the National Oceanic and Atmospheric Administration publishes temperature information of cities around the world in Climates of the world. A random sample of 50 cities gave the data on average average high and low temperature in january shown on the Weis Stats site.  we have to determine and interpret the regression equation for the data.  

Part(c) Step 2: Explanation

Formula used to find the regression equation is   

$\hat{y}=b_0+b_{1}x$

where 

$b_0=-7.5692$

$b_1=0.9168$

therefore,

$\hat{y}=-7.5692+0.9168x$

Part(d) Step 1: Given Information

Given in the question that the National Oceanic and Atmospheric Administration publishes temperature information of cities around the world in Climates of the world. A random sample of 50 cities gave the data on average average high and low temperature in january shown on the Weis Stats site.  we have to  identify the potential outliers and influential observation.  

Part(d) Step 2: Explanation

An outlier is a data point that is far off the regression line.

An influential observation is one where the removal of a point causes a significant change in the regression equation. That instance, removing a point causes a significant shift in the regression line's direction.

There are no potential outliers in the dataset because all of the points are closed to the regression line in the plotted graph. There is no considerable change in the direction of the regression line when a point is removed, hence there are no potentially influencing observations.  

Part(e) Step 1: Given Information

Given in the question that the National Oceanic and Atmospheric Administration publishes temperature information of cities around the world in Climates of the world. A random sample of 50 cities gave the data on average average high and low temperature in january shown on the Weis Stats site.

 we have to obtain  in case a potential outlier is present, remove it and discuss the effect.   

Part(e) Step 2: Explanation

There are no outliers in part d so this is not applicable.  

Part(f) Step 1: Given Information

Given in the question that the National Oceanic and Atmospheric Administration publishes temperature information of cities around the world in Climates of the world. A random sample of 50 cities gave the data on average average high and low temperature in january shown on the Weis Stats site.

we have to obtain in case potential  influential observations is present,remove it and discuss the effect. 

Part(f) Step 2: Explanation

There is no  potential influential observation in part d. so this is not applicable.