Question

Using the data file provided with both variables, x and y, answer the following questions using Excel*:

1.Create a scatterplot with the data. Comment on direction, form, strength, outliers and/or other significant findings.

2.Use the linear model to fit a line to the data and determine the equation ỹ = b₀ + b₁x and Interpret b₀and b₁.

3.Calculate the coefficient of correlation. Discuss the strength of correlation between the explanatory and response variables.

4.Predict the value for ỹ when you choose a value for x. Interpret this solution.

5.Based on the above results, discuss whether the explanatory and response variables are significant.

Total Cigarette Smoking (X)	Unemployment Rate (Y)
9.8	2
12.9	2.3
14.9	2.4
15	2.5
15.1	2.5
15.2	2.6
15.3	2.7
15.4	2.7
15.4	2.7
15.8	2.9
15.8	3
16.1	3.1
16.3	3.2
16.7	3.2
16.8	3.3
16.8	3.3
17.1	3.3
17.1	3.3
17.1	3.4
17.2	3.6
17.3	3.6
17.5	3.7
17.7	3.7
17.8	3.8
17.9	3.9
17.9	4
17.9	4
18	4
18.3	4
18.6	4.1
18.6	4.1
18.8	4.1
19	4.2
19.6	4.2
19.9	4.2
20.2	4.3
20.3	4.3
20.3	4.3
20.4	4.3
20.6	4.3
21.5	4.5
22	4.5
22	4.5
22.1	4.5
22.5	4.7
23.1	4.8
23.1	4.9
23.3	5
25.5	5.7
25.6	5.8
25.6	7.1

Answer 1

1.Create a scatterplot with the data. Comment on direction, form, strength, outliers and/or other significant findings.

1. Brind data in to excel sheet.

2. select data --> go to insert tab --> choose scatter plot diagram

3. Select the data point and add trendline

Direction:

The relationship between Total Cigarette Smoking (X) and Unemployment Rate (Y) is strong, linear, and positive.

Outliers:

A single outliers Y = 7.1

2.Use the linear model to fit a line to the data and determine the equation ỹ = b0 + b1x and Interpret b0and b1.

1. Right click the trnd line of the scatter plot diagram and choose "format trendline". In the format trendline option choose "linaer" and sleect "display equation on chart"

3.Calculate the coefficient of correlation. Discuss the strength of correlation between the explanatory and response variables.

The correlation of coeeficient value is 0.95

a correlation of 0.95 indicates a perfect positive correlation.the data set the points increases the linearity of the given plot

It is a strong relationship between the predictor variable and the response variable leads to a good model.

4.Predict the value for ỹ when you choose a value for x. Interpret this solution

Since we wish to use the equation to predict future values of Y from observations about X, the equation is often shown as: Y’ = a + bX

Where Y’ = the predicted value of Y given a, b and X

The predected value of the above data set as y = 0.284x - 1.4361

5.Based on the above results, discuss whether the explanatory and response variables are significant.

A scatterplot can help you see trends between paired data. If you have both a response variable and an explanatory variable, the explanatory variable is always plotted on the x-axis (the horizontal axis). The response variable is always plotted on the y-axis (the vertical axis).

If you look at the above image, you should be able to tell that wrist size is a very good explanatory variable to predict total cigrette smoking (the response variable)

So the explanatory variable explains or influences changes in a response variable. Both expanatory and response variable are more significant