Final answer:
The subject of this question is Mathematics and it is a High School level question. The independent variable in the multiple regression model is the total floor area, while the dependent variable is the sales price. A scatter plot can be used to visually inspect the relationship between the variables.
Step-by-step explanation:
a. The independent variable is the variable that is being manipulated or controlled by the researcher, in this case, the independent variable is the total floor area. On the other hand, the dependent variable is the variable that is being measured or observed, in this case, the dependent variable is the sales price.
b. To draw a scatter plot of the data, we need to plot the values of the independent variable (total floor area) on the x-axis and the values of the dependent variable (sales price) on the y-axis. Each data point represents a recently sold home in the area.
c. Based on inspection of the scatter plot, we can determine if there is a relationship between the variables. If the data points on the scatter plot show a clear pattern or trend, then there is likely a relationship between the variables. If the data points are randomly scattered, then there may not be a relationship between the variables.
d. To calculate the least-squares line (best-fit line), we use the method of least squares to find the line that minimizes the sum of the squared differences between the actual y-values and the predicted y-values. The equation of the least-squares line is in the form ŷ = a + bx, where ŷ is the predicted sales price, a is the y-intercept, b is the slope, and x is the total floor area.
e. To find the correlation coefficient, we use the formula for correlation, which measures the strength and direction of the linear relationship between two variables. The correlation coefficient ranges from -1 to +1, where -1 represents a strong negative correlation, +1 represents a strong positive correlation, and 0 represents no correlation. If the correlation coefficient is significant (close to -1 or +1), then there is a strong relationship between the variables.
f. To find the estimated sale price for a 32-inch television, we substitute the given value of the independent variable (32) into the equation of the least-squares line. To find the cost for a 50-inch television, we substitute the given value of the independent variable (50) into the equation of the least-squares line.
g. Whether a line is the best way to fit the data depends on the pattern or trend observed in the scatter plot. If the data points show a clear linear relationship, then a line may be the best way to fit the data. However, if the data points do not follow a linear pattern, then a line may not be the best way to fit the data.
h. To determine if there are outliers in the data, we can look for data points that are significantly different from the other data points. Outliers can affect the least-squares line and the correlation coefficient.
i. The slope of the least-squares line represents the change in the dependent variable (sales price) for a one-unit increase in the independent variable (total floor area). For every one-unit increase in the total floor area, the sales price is expected to increase/decrease by the value of the slope.