Question

3 a. describe the association between the two variables.
b. describe any unusual points in your scatterplot
4 a. write the equation that describes the relationship between the number of spaces from go and the cost of the properties.
b. interpret the slope in terms of the context.
c. interpret the y - intercept. does it have a meaning in this context? explain your reasoning.
5 interpret the correlation coefficient.
6 what is the meaning of the coefficient of determination, r²?

Explanation:

Step1: Analyze scatter - plot relationship

The scatter - plot shows a linear relationship between the number of spaces from GO and the cost of properties. The points generally follow a straight - line pattern, indicating a linear association.

Step2: Identify unusual points

Unusual points are outliers. If there are points that deviate significantly from the general pattern of the other points, they are considered unusual. But the description in the image just mentions "5 - 4 black dots" which is unclear. In a proper analysis, we would look for points far from the regression line.

Step3: Interpret regression equation

The equation $\hat{y}=70.1216 + 6.828x$ is in the form of a simple linear regression equation $\hat{y}=b_0 + b_1x$, where $b_0 = 70.1216$ is the y - intercept and $b_1=6.828$ is the slope. The slope means that for each additional space from GO, the cost of the property increases by 6.828 units (the unit of cost is not specified). The y - intercept represents the cost when the number of spaces from GO is 0.

Step4: Interpret correlation coefficient

The correlation coefficient measures the strength and direction of the linear relationship between two variables. A positive correlation coefficient indicates a positive linear relationship (as one variable increases, the other tends to increase), and its value ranges from - 1 to 1. A value close to 1 indicates a strong positive linear relationship, while a value close to 0 indicates a weak or no linear relationship.

Step5: Interpret coefficient of determination

The coefficient of determination $r^{2}$ represents the proportion of the variance in the dependent variable (cost of properties) that is predictable from the independent variable (number of spaces from GO). For example, if $r^{2}=0.76$, it means that 76% of the variation in the cost of properties can be explained by the linear relationship with the number of spaces from GO.

Answer:

3a. The relationship between the two variables is a strong positive linear relationship.
3b. The description of unusual points in the given text is unclear. In a proper analysis, outliers (points far from the regression line) would be considered unusual.
4a. $\hat{y}=70.1216 + 6.828x$
4b. For each additional space from GO, the cost of the property increases by 6.828 units.
4c. The y - intercept 70.1216 represents the cost of the property when the number of spaces from GO is 0.

1. The correlation coefficient measures the strength and direction of the linear relationship between the number of spaces from GO and the cost of properties. A positive value indicates a positive linear relationship, and its magnitude indicates the strength.
2. The coefficient of determination $r^{2}$ represents the proportion of the variance in the cost of properties that can be explained by the linear relationship with the number of spaces from GO.