Answer
Section 1
The relation between marks of both chapters.
Marks of both chapters are positively associated.
The scatter diagram is used to find the correlation between two variables
and it conveys how closely the independent and dependent variables are related with each
other. The steps to create scatter diagram in Excel are as follows:
Step 1: Insert the provided data in the Excel spreadsheet.
Step 2: Select the data and go to insert in the menu bar. Select scatter and then
choose appropriate representation of the scatter diagram.
Step 3: The scatter diagram is constructed.
Step 4: Select Chart area and then click on Design. Click on Chart element to add the axes title and the chart title.
Section 2
The scores of two chapters.
The least-squares linear regression can be obtained as \[\hat{y}=0.7712x+13.839\] and \[{{\text{R}}^{2}}\] is 0.4751.
The Chapter 2 score, x, is the independent variable and Chapter 3 score, y, is the dependent variable.
To obtain the linear regression line for the provided data, Excel is used. The following steps are followed to obtain the regression equation.
Step 1: Select Scatter Plot area drawn in part (a) and Select Trendline. Select More Options.
Step 2: Select the linear model and mark the check box against display equation on chart.
The least-squares regression equation and the scatter diagram for the provided data set is obtained as follows:
Therefore, the least-squares linear regression is obtained as \[\hat{y}=0.7712x+13.839\] and \[{{\text{R}}^{2}}\] is 0.4751.
Section 3
The residual plot is as shown below:
To obtain the residual plot for the model against the explanatory variable, Excel is used. The steps given below are followed for obtaining the plot:
Step 1: Go to data in the menu bar. Click on option Data Analysis and select Regression from the options as shown below:
Step 2: Click “ok” in the above screenshot. A dialog box opens. Enter the range for “Input Y range” and “Input X range” as shown below. Tick labels and Residual plots and select any empty cell for the output range.
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Step 3: Click OK to get the residual plot. The residual plot is shown below:
The variables are linearly related as there is no pattern in errors. Also, with the increase in y and x, the residual value does not get affected much. So, the linear model is appropriate.
But, the observation value \[\left( 33.3,45.7 \right)\] can be termed as an outlier because it is far from the other values.
There is a positive association between marks of both chapters.
From the above analysis, it can be said that if Chapter 2 marks increase, Chapter 3 marks also increase. Hence, Chapter 2 plays an important role in understanding of Chapter 3.
Work Step by Step
Given above.
