Question

2. The following data was gathered by Taxon Auto to model the relationship between automobile weight and miles per gallon.

Weight (lbs) MPG 1759 44 1500 44 1752 40 1980 37 1797 37 2199 34 2404 35 2611 32 3136 29 2606 28 2580 26 2507 26

a. Which variable is the dependent or response variable?

b. Which is the independent or explanatory variable?

Enter the data into an Excel spreadsheet.

c. Create a scatterplot

i. Interpret your scatterplot

ii. Based on the scatterplot - does it appear that linear regression would be a useful tool for prediction of ridership?

Regardless of your answer to c. Run the regression analysis in Excel and use the output to answer the following questions:

d. What is the value of the correlation coefficient? How would you interpret it?

e. What is the value of the coefficient of determination? How would you interpret it?

f. Write the hypotheses for the test of the slope.

g. What is the p-value for the test of the slope? What is your conclusion based on this result?

h. What is the regression formula the represents the relationship between auto weight and MPG?

i. Use your formula to predict the MPG for a car that weighs 3500 pounds. (show formula)

j. Use your formula to predict the MPG for a car that weighs 2100 pounds. (show formula)

Answer 1

a)

dependent -MPG

b)  independent or explanatory variable -weight

c)i)

above is a scatterplot of MPG on vertical Y axis and weight on horizontal axis which shows their corresponding joint relation on different points,

ii)there appears to be a negative linear relationship between MPG and weight and association seems to be useful in prediction

below is regression output of above data from excel\

Regression Statistics
Multiple R	0.8659
R Square	0.7497
Adjusted R Square	0.7247
Standard Error	3.3433
Observations	12.0000
ANOVA
	df	SS	MS	F	Significance F
Regression	1	334.8882	334.8882	29.9600	0.0003
Residual	10	111.7784	11.1778
Total	11	446.6667
	Coefficients	Standard Error	t Stat	P-value	Lower 95%	Upper 95%	Lower 95.0%	Upper 95.0%
Intercept	59.8536	4.7613	12.5709	0.0000	49.2448	70.4625	49.2448	70.4625
weight	-0.0114	0.0021	-5.4736	0.0003	-0.0161	-0.0068	-0.0161	-0.0068

d)

value of the correlation coefficient =-0.8659

as it is negative and its value is near to 1;

this shows that there is a negative linear relationship between weight and mpg

e) coefficient of determination=0.7497

this shows that 74.97% variation in mpg can be explained by variation in weight

f)

hypotheses for the test of the slope: Ho: 1 =0

Ha: 1 0

g)

p value =0.0000

as p value is signifcantly low we reject null hypothesis and conclude that there is a significant linear relationship between weight and mpg

h)

regression formula: mpg =59.8536-0.0114*weight

i)

predicted mpg=59.8536-0.0114*3500 =19.9536

j)

predicted mpg=59.8536-0.0114*2100 =35.9136