Question

You have to write Statistics report of two pages using methods mentioned below-

0) Intro explains the value of the report and the goal (1) Show the prediction equation (2) Explain the range of usable values for the prediction (3)Explain the slope (4) Determine whether the slope is significant (5) Specify the alpha used (6) Correlation explained (7)Standard error for the model explained (8) Justifies the model was appropriate (9) Calculates the prediction requested (10) Discusses the error of the prediction

You can use R studio to calculate all the above-

Captain Buck Tooth has taken you prisoner aboard his pirate ship, the Lucky Lemon. He sees from your college transcripts you have taken a couple of statistics courses. For the last 20 ships he has looted he measured the height in inches when the ship was still way off on the horizon. The captain also has a good memory and remembers how much gold was taken from each ship in number of pieces (data is listed below). Captain Buck Tooth wants you to help him understand the relationship between the size of the ship and the amount of gold it has. As you prepare your report the captain announces he has just seen a ship with a height of 4.1 and he asks you to include in your report how much gold it will have.

The captain hates all tables, graphs, and figures, so you are not allowed to use any of them in your report. If you can’t justify your conclusions you will be fired. From a cannon.

Ship	Gold
4.8	119
1.4	76
3.2	64
2.9	124
1.6	88
1.5	124
3.5	100
2.1	100
2.3	67
3.0	173
2.6	123
1.1	107
1.8	65
4.2	200
4.0	170
2.8	113
4.3	158
2.7	145
4.0	120
2.0	92

Answer 1

Soln

Steps for Regression in Excel

• Import the data in Excel
• In Data Analysis tool from Data Tab.
• Click on regression and select the Y values and X values. Select Labels and click OK.

Regression Output

0)

We are interested in determining the number of pieces of gold taken from ships using the height in inches when the ship was still way off on the horizon

1)

Regression Equation

Gold = 38.95*Ship

3)

Interpretation of Slope

For every one unit increase in Ship height (Independent variable), the dependent variable increases by 38.95 units.

4)

Independent Variable: Ship Height

Alpha = 0.05

Null and Alternate Hypothesis

H₀: The coefficient of independent variable is zero ie the independent variable is insignificant

H_a: The coefficient of independent variable is not zero ie the independent variable is significant

Test Statistic

t = 13.42

P-value < 0.001

Decision Rule

If p-value is less than 0.05, reject the null hypothesis.

Alpha = 0.05

Conclusion

Since the p-value is less than 0.05, hence we reject the null hypothesis. ie the independent variable is significant.

5)

We used alpha = 0.05

6)

Correlation Coefficient = 0.9511

Correlation coefficient indicates high positive correlation between the two variables ie when one variable increases, another also increases and vice versa.

7)

Standard Error = 38.7070

standard error of the regression tells us how wrong the regression model is on average using the units of the response variable

8)

Significance of Model

Alpha = 0.05

Null and Alternate Hypothesis

H₀: All the coefficients are zero (ie the model is not significant)

H_a: At least one of the coefficients is not zero (ie the model is significant)

Test Statistic

F = 180.08

p-value < 0.01

Conclusion

From the ANOVA table, since the p-value is less than 0.05, hence we reject the null hypothesis ie the model is significant.

9)

When Ship Height = 4.1

Gold = 38.95*4.1 = 159.70

10)

95% CI

Lower Bound

Gold = 32.87* Ship

So, Ship Height = 4.1

Gold = 32.87* 4.1 = 134.77

Upper Bound

Gold = 45.02* Ship

So, Ship Height = 4.1

Gold = 45.02* 4.1 = 184.58