Regression/Deviation Homework - Direction, Strength, Slope & Intercept

• Calculator14
In summary, regression analysis is a statistical method used to analyze the relationship between variables, determine direction and significance, and make predictions. Deviation measures how much a data point differs from the mean. The direction in regression analysis is determined by the correlation coefficient. The strength indicates how well the data fits the regression line. The slope represents the rate of change and the intercept represents the value of the dependent variable at zero.
Calculator14

Homework Statement

Data were obtained on watermelon plants; variables of interest were the depth of the roots (inches) and the weight of the watermelon (ounces). A total of 100 plants were measured, with the following summary results: depth mean = 16, weight mean = 75, depth standard deviation = 8, weight standard deviation = 20, and correlation = 0.68. Assume that the relationship is linear. [10 points total]

a. Describe the relationship’s direction and strength. [2 points]
b. Determine the value for the slope of the least squares regression line for predicting weight.
c. Determine the value for the intercept of this least squares regression line.
d. State this regression equation.
e. When the roots are 20 inches deep, predict the watermelon weight.
f. One of the data points was depth = 20, weight = 86. Find the residual for this point.
g. Give the coordinates for two points that are on the regression line. [2 points]
h. If we formed the regression equation to predict root depth, would the resulting regression line have the same slope? (Yes or No)

Homework Equations

I THINK I know a variety of the equations I have to use, for I usually am given a data table to work with. Please help, the wording is very confusing and I have been on this question for two hours.

The Attempt at a Solution

the direction is positive for a. and I am not sure about it's strength but I do know it is 68%
b = a (sy/sx) for b.?
For number c. I understand I have to find b but I am not sure how due to the wording

I think h. is yes but I am not sure :/

Last edited:

a. The direction of the relationship is positive, meaning that as the depth of the roots increases, the weight of the watermelon also increases. The strength of the relationship is moderate, with a correlation coefficient of 0.68.

b. To determine the slope of the least squares regression line, you can use the formula b = r (Sy/Sx), where b is the slope, r is the correlation coefficient, Sy is the standard deviation of the dependent variable (weight), and Sx is the standard deviation of the independent variable (depth). Plugging in the values, we get b = 0.68 * (20/8) = 1.7.

c. To determine the intercept of the least squares regression line, you can use the formula a = y - bx, where a is the intercept, y is the mean of the dependent variable (weight), b is the slope, and x is the mean of the independent variable (depth). Plugging in the values, we get a = 75 - (1.7 * 16) = 48.8.

d. The regression equation is y = 48.8 + 1.7x, where y is the predicted weight and x is the depth of the roots.

e. When the roots are 20 inches deep, the predicted weight would be y = 48.8 + (1.7 * 20) = 81.8 ounces.

f. To find the residual, you need to first calculate the predicted weight using the regression equation. In this case, the predicted weight would be y = 48.8 + (1.7 * 20) = 81.8 ounces. The residual is then the difference between the actual weight (86 ounces) and the predicted weight (81.8 ounces), which is 4.2 ounces.

g. Two points on the regression line would be (16, 75) and (20, 81.8). These coordinates represent the mean values for depth and weight, and the predicted weight for a depth of 20 inches, respectively.

h. No, the slope of the regression line to predict root depth would be different. This is because the regression line is based on the relationship between depth and weight, and switching the variables would result in a different slope.

1. What is regression analysis?

Regression analysis is a statistical method used to analyze the relationship between two or more variables. It is used to determine the strength, direction, and significance of the relationship between the variables, as well as to make predictions about future values.

2. What is deviation?

Deviation is a measure of how much a data point differs from the mean or average value in a dataset. It is calculated by subtracting the mean from the data point and can be positive or negative.

3. How is direction determined in regression analysis?

The direction of the relationship between two variables in regression analysis is determined by the sign of the correlation coefficient. A positive correlation coefficient indicates a positive relationship, while a negative correlation coefficient indicates a negative relationship.

4. What does the strength of a regression analysis indicate?

The strength of a regression analysis indicates how well the data points fit the regression line or curve. It is measured by the value of the correlation coefficient, with a higher value indicating a stronger relationship between the variables.

5. What do the slope and intercept represent in a regression analysis?

The slope in a regression analysis represents the rate of change or the steepness of the regression line or curve. The intercept represents the value of the dependent variable when the independent variable is equal to zero.

• General Math
Replies
4
Views
741
• STEM Educators and Teaching
Replies
11
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
2
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
23
Views
3K
• Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
• Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
• General Math
Replies
8
Views
2K
• Set Theory, Logic, Probability, Statistics
Replies
4
Views
1K
• General Math
Replies
1
Views
963
• Engineering and Comp Sci Homework Help
Replies
2
Views
4K