The scatter plot represents the weight of a car and its gas mileage. Based on the data presented, which statement is true?
(1 point)
Responses
The heaviest car gets the best gas mileage.
The heaviest car gets the best gas mileage.
The lightest car gets the worst gas mileage.
The lightest car gets the worst gas mileage.
Gas mileage decreases with a decrease in car weight.
Gas mileage decreases with a decrease in car weight.
Gas mileage decreases with an increase in car weight.
Gas mileage decreases with an increase in car weight.
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Gas mileage decreases with an increase in car weight.
Desmos Graphing Calculator: Use the link to access the Graphing Calculator. Open a table and input the data. Ask the calculator for a Linear Regression Line (Line of Best Fit)
(3 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
A. What is the equation for the Linear Regression Line? Response area
B. There is a Response area correlation between the test marks and the homework marks.
C. The slope of the line of best fit can be used to make a probabilistic interpretation that states Response area
I'm sorry, I can't access the internet to open the Graphing Calculator. However, I can provide you with the steps to find the equation for the Linear Regression Line manually using the given data in the scatter plot.
1. Input the data into a table.
2. Determine the independent variable (car weight) and the dependent variable (gas mileage).
3. Calculate the sum of the car weights, the sum of the gas mileage, the sum of the products of car weight and gas mileage, the sum of the car weight squared, and the number of data points.
4. Use the formulas for the slope and y-intercept of the line of best fit:
Slope (m) = (n * Σ(xy) - Σx * Σy) / (n * Σ(x^2) - (Σx)^2)
Y-intercept (b) = (Σy - m * Σx) / n
where n is the number of data points, Σxy is the sum of the products of car weight and gas mileage, Σx and Σy are the sums of car weight and gas mileage respectively, and Σ(x^2) is the sum of car weight squared.
5. Substitute the values into the equations to find the slope and y-intercept.
6. Write the equation for the linear regression line in the form y = mx + b, where m is the slope and b is the y-intercept.
Once you have calculated the equation for the Linear Regression Line, you can answer question A by providing the equation in the response area.
For question B, you can determine the correlation by looking at the value of the coefficient of determination (r^2). If the value is close to 1, there is a strong correlation. If it is close to 0, there is a weak correlation. You can calculate the coefficient of determination using the formula:
r^2 = (Σ(xy) - (Σx * Σy) / n) / (√((Σ(x^2) - (Σx)^2 / n) * (∑(y^2) - (Σy)^2 / n))
Once you have calculated the value of r^2, you can answer question B by providing the appropriate response in the response area.
For question C, you have to interpret the slope of the line of best fit. The slope represents the rate of change in the dependent variable (gas mileage) for a one-unit increase in the independent variable (car weight). You can make a probabilistic interpretation by saying that for every one-unit increase in car weight, the gas mileage is expected to decrease by the slope value. You can provide the appropriate response in the response area.
Based on the data presented, the statement "Gas mileage decreases with an increase in car weight" is true.
To determine which statement is true based on the scatter plot representing the weight of a car and its gas mileage, you need to analyze the pattern of the data points on the plot.
Firstly, observe the general trend of the points on the scatter plot. Are they moving in a particular direction? If the points are mostly moving in an upward direction as weight increases, it suggests that there is a positive relationship between weight and gas mileage. On the other hand, if the points are mostly moving in a downward direction as weight increases, it suggests a negative relationship between weight and gas mileage.
Additionally, you can look for any clusters or patterns formed by the data points. Are there any distinct clusters of points that indicate potential groups or categories? This can provide additional insights into the relationship between weight and gas mileage.
Finally, consider any outliers or unusual data points on the scatter plot. Do these outliers impact the overall trend or pattern? Sometimes outliers can skew the relationship between the variables, so it's important to take them into account.
By analyzing these factors, you can determine which statement is true based on the scatter plot data.