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.

Short 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

Step-by-step solution

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.