Question

3. An engineer wanted to determine how the weight of a car (kilograms), ?, affects fuel consumption (kilometers per litre), ?. The weights and fuel consumption for a random sample of 10 cars were recorded. Refer to the regression results from Excel.

Regression Statistics

Multiple R	0.84157604
R Square	0.708250231
Adjusted R Square	0.671781509
Standard Error	0.712010044
Observations	10

  

	Coefficients	Standard Error	t-Stat	P-Value	Lower 95%	Upper 95%
Intercept	15.883033	1.680071	9.453785	0.000013	12.008782	19.757285
X-Variable 1	-0.004384	0.000995	(?)	0.002266	-0.006679	-0.002090

a) Write the equation of the estimated least-squares regression line.

b) Test whether a linear relationship exists between weight of a car and fuel consumption at the
? = 0.01 level of significance. Use the critical value method.

c) Use the Excel output to write a 95% confidence interval for the slope of the true least-squares regression line. Interpret the result. Write a descriptive statement that could be easily understood by someone who is not in this statistics class.

d) A 95% prediction interval for ? = 1900 is 5.83 to 9.28. Interpret this result. Write a descriptive
statement that could be easily understood by someone who is not in this statistics class.

Answer 1

a) Write the equation of the estimated least-squares regression line.

The equation of the estimated least-squares regression line is:

y = 15.883033 + 0.004384*x

b) Test whether a linear relationship exists between weight of a car and fuel consumption at the
? = 0.01 level of significance. Use the critical value method.

The hypothesis being tested is:

H0: ρ = 0

Ha: ρ ≠ 0

Pearson's r is 0.84157604.

The critical r-value for ? = 0.01 and df = 8 is 0.765.

Since 0.84157604 > 0.765, we can reject the null hypothesis.

Therefore, we can conclude that there is a linear relationship between the weight of a car and fuel consumption.

c) Use the Excel output to write a 95% confidence interval for the slope of the true least-squares regression line. Interpret the result. Write a descriptive statement that could be easily understood by someone who is not in this statistics class.

The 95% confidence interval for the slope of the true least-squares regression line is between -0.006679 and

-0.002090. We are 95% confident that the true slope of the true least-squares regression line is between -0.006679 and -0.002090. The model can be trusted to get the relationship with the weight of a car and fuel consumption.

d) A 95% prediction interval for ? = 1900 is 5.83 to 9.28. Interpret this result. Write a descriptive
statement that could be easily understood by someone who is not in this statistics class.

We are 95% confident that the new observation will fall between 5.83 and 9.28.

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