Question

predicted fuel economy for a can that has 175 horsepower, 14.2 quarter mile time and 6 cylinders make predictions using the regression model. address the following questions in your analysis:

Answer 1

To predict fuel economy using a regression model, consider the variables that affect it. Use the line of best fit from the regression analysis to make predictions. Analyze the scatter plot for outliers and assess the relationship between fuel efficiency and weight using the correlation coefficient.

Step-by-step explanation:

To predict fuel economy using a regression model, we need to consider the variables that affect it. In this case, we have horsepower, quarter mile time, and the number of cylinders. The regression model will provide us with a line of best fit that represents the relationship between these variables and fuel economy. We can use this line to make predictions for specific values.

1. To determine the practical interpretation of the slope of the least-squares line, we need to consider the relationship between fuel efficiency and weight. A positive slope would indicate a positive relationship, meaning that as weight increases, fuel efficiency also increases. On the other hand, a negative slope would suggest a negative relationship, where fuel efficiency decreases as weight increases.
2. Using the regression model, we can predict the fuel efficiency of a car that weighs 4,000 pounds by finding the corresponding point on the line of best fit. We input the weight (4,000 pounds) into the regression equation and calculate the predicted fuel efficiency.
3. While we can use the least-squares line to predict fuel efficiency for a range of weights, it is important to consider the range of weights included in the data set used to create the regression model. If the weights in the data set do not cover the range of 10,000 pounds, the prediction for a car weighing 10,000 pounds may not be accurate.
4. a. To determine if the line fits the data, we can analyze the scatter plot of the data points and the line of best fit. If the points are closely clustered around the line and there are no significant deviations or outliers, then the line seems to fit the data. If there are large deviations or outliers, the line may not accurately represent the relationship between the variables.
5. b. The correlation between fuel efficiency and weight of a car can be determined by the regression analysis. If the correlation coefficient (r-value) is close to 1 or -1, it indicates a strong positive or negative correlation, respectively. If the r-value is close to 0, there is little to no correlation. The correlation coefficient helps us understand the strength and direction of the relationship between fuel efficiency and weight.
6. If there are any outliers in the data, they can be identified by analyzing the scatter plot of the data points. Outliers are points that deviate significantly from the overall pattern of the data and can affect the line of best fit.