78. The average number of people in a family that attended college for various years is given in Table 12.30.Year Number of Family Members Attending College1969 4.01973 3.61975 3.21979 3.01983 3.01988 3.01991 2.9Table 12.30a. Using “year” as the independent variable and “Number of Family Members Attending College” as thedependent variable, draw a scatter plot of the data.b. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bxc. Find the correlation coefficient. Is it significant?d. Pick two years between 1969 and 1991 and find the estimated number of family members attending college.e. Based on the data in Table 12.30, is there a linear relationship between the year and the average number offamily members attending college?f. Using the least-squares line, estimate the number of family members attending college for 1960 and 1995.Does the least-squares line give an accurate estimate for those years? Explain why or why not.g. Are there any outliers in the data?h. What is the estimated average number of family members attending college for 1986? Does the least squaresline give an accurate estimate for that year? Explain why or why not.i. What is the slope of the least squares (best-fit) line? Interpret the slope.
78. The average number of people in a family that attended college for various years is given in Table 12.30.Year Number of Family Members Attending College1969 4.01973 3.61975 3.21979 3.01983 3.01988 3.01991 2.9Table 12.30a. Using “year” as the independent variable and “Number of Family Members Attending College” as thedependent variable, draw a scatter plot of the data.b. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bxc. Find the correlation coefficient. Is it significant?d. Pick two years between 1969 and 1991 and find the estimated number of family members attending college.e. Based on the data in Table 12.30, is there a linear relationship between the year and the average number offamily members attending college?f. Using the least-squares line, estimate the number of family members attending college for 1960 and 1995.Does the least-squares line give an accurate estimate for those years? Explain why or why not.g. Are there any outliers in the data?h. What is the estimated average number of family members attending college for 1986? Does the least squaresline give an accurate estimate for that year? Explain why or why not.i. What is the slope of the least squares (best-fit) line? Interpret the slope.
78. The average number of people in a family that attended college for various years is given in Table 12.30.Year Number of Family Members Attending College1969 4.01973 3.61975 3.21979 3.01983 3.01988 3.01991 2.9Table 12.30a. Using “year” as the independent variable and “Number of Family Members Attending College” as thedependent variable, draw a scatter plot of the data.b. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bxc. Find the correlation coefficient. Is it significant?d. Pick two years between 1969 and 1991 and find the estimated number of family members attending college.e. Based on the data in Table 12.30, is there a linear relationship between the year and the average number offamily members attending college?f. Using the least-squares line, estimate the number of family members attending college for 1960 and 1995.Does the least-squares line give an accurate estimate for those years? Explain why or why not.g. Are there any outliers in the data?h. What is the estimated average number of family members attending college for 1986? Does the least squaresline give an accurate estimate for that year? Explain why or why not.i. What is the slope of the least squares (best-fit) line? Interpret the slope.
78. The average number of people in a family that attended college for various years is given in Table 12.30. Year Number of Family Members Attending College 1969 4.0 1973 3.6 1975 3.2 1979 3.0 1983 3.0 1988 3.0 1991 2.9 Table 12.30 a. Using “year” as the independent variable and “Number of Family Members Attending College” as the dependent variable, draw a scatter plot of the data. b. Calculate the least-squares line. Put the equation in the form of: ŷ = a + bx c. Find the correlation coefficient. Is it significant? d. Pick two years between 1969 and 1991 and find the estimated number of family members attending college. e. Based on the data in Table 12.30, is there a linear relationship between the year and the average number of family members attending college? f. Using the least-squares line, estimate the number of family members attending college for 1960 and 1995. Does the least-squares line give an accurate estimate for those years? Explain why or why not. g. Are there any outliers in the data? h. What is the estimated average number of family members attending college for 1986? Does the least squares line give an accurate estimate for that year? Explain why or why not. i. What is the slope of the least squares (best-fit) line? Interpret the slope.
Definition Definition Statistical measure used to assess the strength and direction of relationships between two variables. Correlation coefficients range between -1 and 1. A coefficient value of 0 indicates that there is no relationship between the variables, whereas a -1 or 1 indicates that there is a perfect negative or positive correlation.
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