The lines of best fit for various bivariate data sets are given below. Using the line of best fit, predict the value of y that corresponds to the given x-value, correct to two decimal places:
y = 3.36x; x = 9
y = -1.52x+1.32; x = 5
y = 43.26x+8.74; x = 0.6
y = -0.88x-0.97; x = -19.12
y = 8.84 x; x = 7.68
y = - 8.71 x + 6.79; x = 3.49
y = 22.42 x + 2.93; x = 0.26
y = - 0.84 x - 0.19; x = -43.15
The lines of best fit for various bivariate data sets are given below. Using the line of best fit, predict the value of x that corresponds to the given y-value, correct to two decimal places:
y = 6x; y = 24
y = 6x-7; y = 5
y = -8.63x-5.84; y = 40
y = 0.72x+1.47; y = 1.8
y = 9.23 x - 4.18; y = 24.8945
y = - 7.76 x - 5.89; y = 713.7724
y = - 6.83 x; y = - 59.6259
y = 0.45 x + 7.62; y = 7.566
A bivariate data set has a line of best fit with equation t = 4.24 s.
Predict the value of t when s = 3.76.
A bivariate data set has a line of best fit with equation B = - 3.37 A + 9.87.
Predict the value of B when A = 8.26.
A bivariate data set has a line of best fit with equation u = - 9.12 v - 6.93.
Find the value of v that gives a prediction of u = 575.6556.
For each of the following data sets:
Use technology to find the equation of the line of best fit.
Use the line of best fit to calculate the y-value for each of the given x-values.
x = 14
| x | 1 | 3 | 4 | 5 | 7 | 9 | 12 | 13 | 16 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | -1 | 0 | 3 | 3 | 4 | 5 | 5 | 7 | 9 | 10 |
x = 69
| x | 36 | 51 | 50 | 41 | 44 | 47 | 58 | 59 | 37 | 43 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 88 | 50 | 53 | 95 | 50 | 64 | 23 | 6 | 85 | 83 |
For each of the data sets below, determine whether the prediction is an extrapolation or an interpolation:
A prediction of y when x = 5
| x | 4 | 7 | 8 | 11 | 12 | 13 | 17 | 18 | 19 | 20 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 0 | 2 | 4 | 7 | 6 | 4 | 8 | 8 | 11 | 8 |
A prediction of y when x = 33
| x | 37 | 54 | 58 | 59 | 43 | 55 | 60 | 38 | 64 | 35 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 72 | 53 | 26 | 21 | 73 | 47 | 12 | 102 | 10 | 112 |
A prediction of y when x = 14
| x | 1 | 3 | 4 | 5 | 7 | 9 | 12 | 13 | 16 | 19 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | -1 | 0 | 3 | 3 | 4 | 5 | 5 | 7 | 9 | 10 |
A prediction of y when x = 69
| x | 36 | 51 | 50 | 41 | 44 | 47 | 58 | 59 | 37 | 43 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 88 | 50 | 53 | 95 | 50 | 64 | 23 | 6 | 85 | 83 |
For each of the data sets below, determine whether the prediction is an extrapolation or an interpolation:
A prediction of y = 95.69 is made from the following data set using the line of best fit with equation y = - 0.07 x + 96.18.
| x | 19 | 10 | 1 | 7 | 14 | 11 | 2 | 5 | 17 | 8 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 94 | 94.4 | 97 | 96.4 | 94.4 | 97.8 | 94.9 | 95.9 | 96 | 94.4 |
A prediction of y = 72.77 is made from the following data set using the line of best fit with equation y = 1.26 x - 57.01.
| x | 93 | 57 | 86 | 97 | 78 | 96 | 68 | 69 | 54 | 92 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 51.2 | 25.4 | 38.9 | 58.6 | 38.2 | 60.8 | 26.3 | 28.5 | 5.4 | 92 |
A prediction of y = 95.7 is made from the following data set using the line of best fit with equation y = -0.15 x +97.8.
| x | 4 | 6 | 1 | 15 | 10 | 5 | 7 | 2 | 9 | 3 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 96.7 | 97.3 | 97.7 | 94 | 96.9 | 98.5 | 97.3 | 95.3 | 97.5 | 97.5 |
A prediction of y = 63.37 is made from the following data set using the line of best fit with equation y = 0.79 x -20.37.
| x | 4 | 6 | 1 | 15 | 10 | 5 | 7 | 2 | 9 | 3 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 96.7 | 97.3 | 97.7 | 94 | 96.9 | 98.5 | 97.3 | 95.3 | 97.5 | 97.5 |
Predict the value of y for the given x-value.
Comment on whether the prediction is reliable, referring to both the strength of correlation and whether interpolation or extrapolation is used.
Correlation coefficient: r = 0.93, x = 15, line of best fit: y = 0.84 x + 2.66.
| x | 10 | 7 | 14 | 1 | 6 | 13 | 19 | 5 | 20 | 9 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 9 | 10 | 14 | 3 | 6 | 10 | 19 | 9 | 21 | 13 |
Correlation coefficient: r = 0.46, x = 49, line of best fit: y = 0.64 x + 54.31.
| x | 37 | 33 | 52 | 100 | 65 | 81 | 83 | 18 | 59 | 51 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 47.6 | 36.4 | 145.6 | 137 | 74 | 93.8 | 78.4 | 82.4 | 101.2 | 117.3 |
Correlation coefficient: r = - 1, x = 1, line of best fit: y = - 3.06 x + 93.51.
| x | 48 | 96 | 99 | 51 | 43 | 42 | 82 | 85 | 69 |
|---|---|---|---|---|---|---|---|---|---|
| y | -45 | -202 | -213 | -72 | -37 | -38 | -163 | -156 | -113 |
Correlation coefficient: r = 0.45, x = 143, line of best fit: y = 0.22 x + 0.7.
| x | 23 | 81 | 11 | 44 | 50 | 91 | 51 | 95 | 53 | 82 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 1 | 35.2 | 1 | 12.8 | 23 | 1.7 | 21.2 | 35 | 1 | 2.9 |
Correlation coefficient: r = 0.91, x = 9, line of best fit: y = 0.8 x + 0.36.
| x | 9 | 14 | 6 | 1 | 2 | 10 | 5 | 17 | 16 | 3 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 6 | 16 | 6 | 3 | 3 | 8 | 2 | 12 | 13 | 1 |
Correlation coefficient: r = -0.43, x = 45, line of best fit: y = -0.63 x + 127.89.
| x | 50 | 85 | 17 | 52 | 65 | 58 | 28 | 63 | 83 | 93 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 49 | 32 | 146.6 | 138.6 | 72 | 98.9 | 89.4 | 76.4 | 96.4 | 105.4 |
Correlation coefficient: r = -0.99, x = 14, line of best fit: y = -2.99 x + 88.56.
| x | 87 | 59 | 92 | 97 | 74 | 45 | 71 | 73 | 76 |
|---|---|---|---|---|---|---|---|---|---|
| y | -168 | -90 | -196 | -201 | -131 | -49 | -116 | -129 | -134 |
Correlation coefficient: r = 0.41, x = 139, line of best fit: y = 0.16 x + 0.74.
| x | 53 | 90 | 45 | 63 | 31 | 16 | 66 | 57 | 55 | 6 |
|---|---|---|---|---|---|---|---|---|---|---|
| y | 24.1 | 9 | 1 | 14.1 | 1 | 1 | 25.2 | 2.4 | 1 | 5.7 |
Research on the average number of cigarettes per day, x, smoked during pregnancy and the birth weight of the newborn baby, y, was conducted. Results are recorded in the adjacent table:
Calculate the correlation coefficient between the two variables. Round your answer to two decimal places.
Describe the statistical relationship between these two variables in terms of strength, direction and shape.
Use technology to find the line of best fit for this data. Round all values to two decimal places.
Use your line of best fit to predict the birth weight of a newborn whose mother smoked 5 cigarettes per day.
Justify the reliability of the prediction.
| x | y |
|---|---|
| 46.30 | 3.90 |
| 13.00 | 5.80 |
| 21.40 | 5.00 |
| 25.00 | 4.80 |
| 8.60 | 5.50 |
| 36.50 | 4.50 |
| 1.00 | 7.00 |
| 17.90 | 5.10 |
| 10.60 | 5.50 |
| 13.40 | 5.10 |
| 37.30 | 3.80 |
| 18.50 | 5.70 |
A sample of families were interviewed about their annual family income and their average monthly expenditure. The results are given in the table below:
Calculate the correlation coefficient between the two variables. Round your answer to two decimal places.
Describe the statistical relationship between these two variables.
Use technology to find the line of best fit for this data. Round all values to three decimal places.
Use your line of best fit to predict the monthly expenditure for a family whose annual income is \$80\,000.
For which of the following annual incomes would the regression line produce the most reliable prediction?
| \text{Income }(x) | \text{Expenditure }(y) |
|---|---|
| 66\,000 | 1100 |
| 75\,000 | 1700 |
| 65\,000 | 1400 |
| 73\,000 | 1300 |
| 54\,000 | 600 |
| 90\,000 | 1800 |
| 87\,000 | 1100 |
| 87\,000 | 1500 |
| 94\,000 | 1800 |
| 96\,000 | 2200 |
The estimated iron ore grades (percentage of iron content) and the actual recovered iron ore grades are recorded to determine the accuracy of the models used by a mining company. The percentages are recorded in the table below:
| \text{Estimated }(x) | 38\% | 32\% | 31\% | 33\% | 38\% | 40\% |
|---|---|---|---|---|---|---|
| \text{Actual }(y) | 48\% | 29\% | 42\% | 32\% | 40\% | 50\% |
Calculate the correlation coefficient between the two variables, rounded to two decimal places.
Describe the statistical relationship between these two variables.
Use technology to find the line of best fit for this data. Round all values to two decimal places.
Use your line of best fit to predict the actual iron ore grade from a pit where the estimated grade is 35\%. Round your answer to two decimal places.
Justify the reliability of this prediction.
A team of salespeople submit their expenses and their sales for the month of March to their manager. Figures are recorded in the adjacent table:
Calculate the correlation coefficient between the two variables. Round your answer to two decimal places.
Describe the statistical relationship between these two variables.
Use technology to find the line of best fit for this data. Round all values to two decimal places.
Use your line line of best fit to predict the expenses of a person in this department who made sales of \$6000 for the month.
Justify the reliability of this prediction.
| \text{Sales (hundreds) }(x) | \text{Expenses }(y) |
|---|---|
| 55.7 | 43.8 |
| 48 | 28.9 |
| 62.7 | 73.9 |
| 23.4 | 11.9 |
| 23.8 | 9 |
| 60.6 | 50 |
| 20.2 | 20.2 |
| 52.1 | 28.2 |
| 23.4 | 19.2 |
| 33.3 | 31.1 |