Question

The following data give the family size (x) and number of pets per family (y) for a random sample of 15 families. Create a scatterplot for the data. Draw: Determine the least squares regression tine for the data. Round values to four decimal places, if necessary. y] = Determine the correlation coefficent. Round the solution to four decimal places, if necessary. F= Use the model to predict the number of pets owned by a family with 1 members. Round the solution to the nearest whole number

Answer 1

To analyze the relationship between family size and number of pets, a scatterplot is drawn followed by the calculation of the least-squares regression line and correlation coefficient to assess the relationship's significance.

Step-by-step explanation:

To investigate the relationship between family size (independent variable) and the number of pets per family (dependent variable), we start by plotting a scatterplot of the given data. This visual representation shows the distribution of data points and allows us to assess any potential correlation visually.

Next, we calculate the least-squares regression line, an equation of the form ŷ = a + bx, where a is the y-intercept and b is the slope. This line minimizes the sum of the squares of the vertical distances (residuals) of the points from the line.

To assess the strength and direction of the linear relationship between the two variables, we find the correlation coefficient, denoted by r. If r is close to 1 or -1, it indicates a significant linear relationship.

Families with different sizes might have varying numbers of pets, and using the regression line, we can predict the expected number of pets for a family of any given size.