119k views
4 votes
In the painting process of refrigerators, thickness of paint layer is expected to be proportional to the spraying time. The table below shows the thickness of the paint layer measured after spraying for different time intervals. Obtain a scatter diagram for the data, showing the best fit trend line and the suitable regression analysis (Determine R,R 2

, scatter plot and error analysis) 1. What is the dependent variable? 2. What is the degree of correlation? 3. What is the type of correlation? 4. What is the strength of correlation? 5. If the spray time is 9 seconds, what is the expected thickness of the paint? Show your calculations. 6. If the thickness is 0.55 mm, what could have been the spray time? Show your calculations.

User Sps
by
7.1k points

1 Answer

5 votes

The dependent variable is the paint layer thickness, and after generating a scatter plot, the degree, type, and strength of correlation are determined through the least-squares line and correlation coefficient. Estimates for specific spray times or thickness values can be obtained by substituting into the regression equation.

In the context of a painting process for refrigerators, where the thickness of the paint layer is expected to be proportional to the spraying time, the dependent variable would be the paint layer thickness, as it depends on the independent variable, which is the spray time. To analyze the relationship, a scatter plot is needed along with a best fit trend line to visualize the data.

A least-squares line can be calculated to fit the data. This line will be in the form ý = a + bx, where ý represents the predicted thickness and x is the spray time. The correlation coefficient, or R, will show the degree of correlation, and its square, R², indicates the strength of correlation. A higher absolute value of R suggests a stronger relationship.

For a specific spray time like 9 seconds, you would plug this value into the regression equation to estimate the expected thickness. Conversely, if given a thickness (e.g., 0.55 mm), you would solve for the spray time by substituting the thickness value into the regression equation and solving for x.

Regarding error analysis, it is important to assess the residuals to understand how well the model fits the data points. Any significant deviations would suggest that factors other than spray time might influence the paint thickness.

User HackerBoss
by
8.7k points

No related questions found