Question

Make a scatter plot from a data set, calculate the linear correlation coefficient, least-squares line of regression, add the line to the plot, analyze the residuals, and make predictions. Type the data for the weight in pounds of various domestic cars and their highway gas mileage (in miles per gallon) in Excel. Type weight in the first cell, and enter the data for weight in the first column (going down). Type mpg at the top of the second column and enter the data for mpg. Save the spreadsheet as a csv (comma separated values) file onto the computer. 3565 3985 3180 3340 3100 3275 2580 3170 2655 3300 20.0 18.0 19.0 21.5 21.0 22.5 27.0 22.0 26.0 20.0 weig mpg 3680 3310 3590 3475 2770 2690 20.5 19.5 20.5 21.0 24.0 26.0 mpg

1. Describe the trend of the data, if any.

2. Calculate the linear correlation coefficient and is the linear correlation coefficient
significant? Why/why not?

3. Find the least-squares line of regression.

4. Graph the regression line on the scatter plot

5. Plot the residuals (give it your own title and labels for the axes!) with lines for 2 standard
deviations of the residuals.

6. Predict the gas mileage of a 2000, 3000 and 4000 lb car.

Answer 1

weight	mpg
3565	20
3985	18
3180	19
3340	21.5
3100	21
3275	22.5
2580	27
3170	22
2655	26
3300	20
3680	20.5
3310	19.5
3590	20.5
3475	21
2770	24
2690	26

SUMMARY OUTPUT
Regression Statistics
Multiple R	0.8718
R Square	0.7600
Adjusted R Square	0.7429
Standard Error	1.3511
Observations	16
ANOVA
	df	SS	MS	F	Significance F
Regression	1	80.9283	80.9283	44.3336	0.0000
Residual	14	25.5561	1.8254
Total	15	106.4844
	Coefficients	Standard Error	t Stat	P-value	Lower 95%
Intercept	40.6142	2.8486	14.2577	0.0000	34.5047
weight	-0.0058	0.0009	-6.6584	0.0000	-0.0077

1. Describe the trend of the data, if any.

There is negative trend 'as weight increases mpg decreases

2. Calculate the linear correlation coefficient and is the linear correlation coefficient
significant? Why/why not?

r = -0.8718

p-value = 0.0000

hence it is significant

3. Find the least-squares line of regression.

y^ = 40.6142 -0.0058 weight

4. Graph the regression line on the scatter plot

mpg 30 20 15 10 500 1500 2500 3000 3500 0 1000 2000 4500