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5.4

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Topic 5 - Statistics and probability » 5.4

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Directly related questions

17N.2.sl.TZ0.8e: Adam decides to increase the number of bees in each low production hive. Research suggests that...
17N.2.sl.TZ0.8d.ii: Find the number of hives that have a high production.
17N.2.sl.TZ0.8d.i: Find the value of \(k\);
17N.2.sl.TZ0.8c: Write down the number of low production hives.
17N.2.sl.TZ0.8b: Use this regression line to estimate the monthly honey production from a hive that has 270 bees.
17N.2.sl.TZ0.8a: Write down the value of \(a\) and of \(b\).
16M.2.sl.TZ1.5b: The equation of the line of best fit is \(\ln M = - 0.12t + 4.67\). Given that...
16M.2.sl.TZ1.5a: State two words that describe the linear correlation between \(\ln M\) and \(t\).
15M.2.sl.TZ2.3a: (i) Find the value of \(a\) and of \(b\). (ii) Write down the value of \(r\).
15M.2.sl.TZ1.1b: Elizabeth watches television for an average of \(3.7\) hours per day. Use your regression line...
15M.2.sl.TZ1.1a: (i) Find the correlation coefficient. (ii) Write down the value of \(a\) and of \(b\).
SPNone.1.sl.TZ0.2a: Write down the possible minimum and maximum values of r .
SPNone.1.sl.TZ0.2b: Given that \(r = 0.95\) , which of the following diagrams best represents the data.
SPNone.1.sl.TZ0.2c: For the data in diagram D , which two of the following expressions describe the correlation...
SPNone.2.sl.TZ0.8a: Write down the equation of the regression line of y on x .
SPNone.2.sl.TZ0.8b(i) and (ii): Use your regression line from part (a) as a model to answer the following. Interpret the meaning...
SPNone.2.sl.TZ0.8c: Estimate the cost of producing 60 boxes.
SPNone.2.sl.TZ0.8d: The factory sells the boxes for $19.99 each. Find the least number of boxes that the factory...
SPNone.2.sl.TZ0.8e(i) and (ii): Comment on the appropriateness of using your model to (i) estimate the cost of producing...
18M.2.sl.TZ2.1b: Use your equation to estimate the mean weight of a child that is 1.95 years old.
18M.2.sl.TZ2.1a.ii: Write down the correlation coefficient.
18M.2.sl.TZ2.1a.i: Find the value of a and of b.
18M.2.sl.TZ1.8c: The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0 , n ≠ 0 ,...
18M.2.sl.TZ1.8b: Use the regression equation to estimate the value of y when x = 3.57.
18M.2.sl.TZ1.8a: Find the value of a and of b.
14M.2.sl.TZ1.3a(i): The relationship between the variables is modelled by the regression equation \(y = ax +...
14M.2.sl.TZ1.3a(ii): The relationship between the variables is modelled by the regression equation \(y = ax +...
14M.2.sl.TZ1.3b(i): Write down the correlation coefficient.
14M.2.sl.TZ1.3b(ii): State which two of the following describe the correlation between the variables. strong ...
14M.2.sl.TZ2.3a(i): Write down the value of \(a\) and of \(b\).
14M.2.sl.TZ2.3a(ii): Explain what the gradient \(a\) represents.
14M.2.sl.TZ2.3b: Use the model to estimate the amount of fuel the car would use if it is driven \(110\) km.
16M.2.sl.TZ2.8d: Find the year when Lina sells her car.
16M.2.sl.TZ2.8c: Calculate the price of Lina’s car after 6 years.
16M.2.sl.TZ2.8b: Use the regression equation to estimate the price of Lina’s car, giving your answer to the...
16M.2.sl.TZ2.8a: (i) Find the correlation coefficient. (ii) Write down the value of \(a\) and of \(b\).
14N.2.sl.TZ0.2a: Find the correlation coefficient.
14N.2.sl.TZ0.2b: The relationship can be modelled by the regression line with equation \(y = ax + b\). Write down...
14N.2.sl.TZ0.2c: Rita scored a total of \(26\) in her IB Diploma. Use your regression line to estimate Rita’s...
15N.2.sl.TZ0.9b: Use the regression equation to estimate the number of coyotes in the reserve when \(t = 7\).
17M.2.sl.TZ2.2b: Use the regression equation to estimate the number of visitors on a day when the maximum...
17M.2.sl.TZ2.2a.ii: Write down the value of \(r\).
17M.2.sl.TZ2.2a.i: Find the value of \(a\) and of \(b\).
17M.1.sl.TZ1.4c: Jim’s model is \(d = - 2.24t + 105\), for \(0 \leqslant t \leqslant 20\). Use his model to...
17M.1.sl.TZ1.4b: Jim describes the correlation as very strong. Circle the value below which best represents the...
17M.1.sl.TZ1.4a.ii: Write down the boiling temperature of the liquid.
17M.1.sl.TZ1.4a.i: Write down the independent variable.

Sub sections and their related questions

Linear correlation of bivariate data.

14M.2.sl.TZ1.3a(i): The relationship between the variables is modelled by the regression equation \(y = ax +...
14M.2.sl.TZ1.3a(ii): The relationship between the variables is modelled by the regression equation \(y = ax +...
14M.2.sl.TZ1.3b(i): Write down the correlation coefficient.
14M.2.sl.TZ1.3b(ii): State which two of the following describe the correlation between the variables. strong ...
14M.2.sl.TZ2.3a(i): Write down the value of \(a\) and of \(b\).
14M.2.sl.TZ2.3a(ii): Explain what the gradient \(a\) represents.
14M.2.sl.TZ2.3b: Use the model to estimate the amount of fuel the car would use if it is driven \(110\) km.
14N.2.sl.TZ0.2a: Find the correlation coefficient.
14N.2.sl.TZ0.2b: The relationship can be modelled by the regression line with equation \(y = ax + b\). Write down...
14N.2.sl.TZ0.2c: Rita scored a total of \(26\) in her IB Diploma. Use your regression line to estimate Rita’s...
15M.2.sl.TZ1.1a: (i) Find the correlation coefficient. (ii) Write down the value of \(a\) and of \(b\).
15M.2.sl.TZ2.3a: (i) Find the value of \(a\) and of \(b\). (ii) Write down the value of \(r\).
15N.2.sl.TZ0.9b: Use the regression equation to estimate the number of coyotes in the reserve when \(t = 7\).
16M.2.sl.TZ2.8a: (i) Find the correlation coefficient. (ii) Write down the value of \(a\) and of \(b\).
16M.2.sl.TZ2.8b: Use the regression equation to estimate the price of Lina’s car, giving your answer to the...
16M.2.sl.TZ2.8c: Calculate the price of Lina’s car after 6 years.
16M.2.sl.TZ2.8d: Find the year when Lina sells her car.
17N.2.sl.TZ0.8a: Write down the value of \(a\) and of \(b\).
17N.2.sl.TZ0.8b: Use this regression line to estimate the monthly honey production from a hive that has 270 bees.
17N.2.sl.TZ0.8c: Write down the number of low production hives.
17N.2.sl.TZ0.8d.i: Find the value of \(k\);
17N.2.sl.TZ0.8d.ii: Find the number of hives that have a high production.
17N.2.sl.TZ0.8e: Adam decides to increase the number of bees in each low production hive. Research suggests that...
18M.2.sl.TZ1.8a: Find the value of a and of b.
18M.2.sl.TZ1.8b: Use the regression equation to estimate the value of y when x = 3.57.
18M.2.sl.TZ1.8c: The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0 , n ≠ 0 ,...
18M.2.sl.TZ2.1a.i: Find the value of a and of b.
18M.2.sl.TZ2.1a.ii: Write down the correlation coefficient.
18M.2.sl.TZ2.1b: Use your equation to estimate the mean weight of a child that is 1.95 years old.

Pearson’s product–moment correlation coefficient \(r\).

SPNone.1.sl.TZ0.2a: Write down the possible minimum and maximum values of r .
SPNone.1.sl.TZ0.2b: Given that \(r = 0.95\) , which of the following diagrams best represents the data.
SPNone.1.sl.TZ0.2c: For the data in diagram D , which two of the following expressions describe the correlation...
14M.2.sl.TZ1.3b(i): Write down the correlation coefficient.
14M.2.sl.TZ1.3b(ii): State which two of the following describe the correlation between the variables. strong ...
14N.2.sl.TZ0.2a: Find the correlation coefficient.
15M.2.sl.TZ1.1a: (i) Find the correlation coefficient. (ii) Write down the value of \(a\) and of \(b\).
15M.2.sl.TZ2.3a: (i) Find the value of \(a\) and of \(b\). (ii) Write down the value of \(r\).
16M.2.sl.TZ2.8a: (i) Find the correlation coefficient. (ii) Write down the value of \(a\) and of \(b\).
16M.2.sl.TZ2.8b: Use the regression equation to estimate the price of Lina’s car, giving your answer to the...
16M.2.sl.TZ2.8c: Calculate the price of Lina’s car after 6 years.
16M.2.sl.TZ2.8d: Find the year when Lina sells her car.
18M.2.sl.TZ1.8a: Find the value of a and of b.
18M.2.sl.TZ1.8b: Use the regression equation to estimate the value of y when x = 3.57.
18M.2.sl.TZ1.8c: The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0 , n ≠ 0 ,...
18M.2.sl.TZ2.1a.i: Find the value of a and of b.
18M.2.sl.TZ2.1a.ii: Write down the correlation coefficient.
18M.2.sl.TZ2.1b: Use your equation to estimate the mean weight of a child that is 1.95 years old.

Scatter diagrams; lines of best fit.

SPNone.1.sl.TZ0.2c: For the data in diagram D , which two of the following expressions describe the correlation...
16M.2.sl.TZ2.8a: (i) Find the correlation coefficient. (ii) Write down the value of \(a\) and of \(b\).
16M.2.sl.TZ2.8b: Use the regression equation to estimate the price of Lina’s car, giving your answer to the...
16M.2.sl.TZ2.8c: Calculate the price of Lina’s car after 6 years.
16M.2.sl.TZ2.8d: Find the year when Lina sells her car.
17N.2.sl.TZ0.8a: Write down the value of \(a\) and of \(b\).
17N.2.sl.TZ0.8b: Use this regression line to estimate the monthly honey production from a hive that has 270 bees.
17N.2.sl.TZ0.8c: Write down the number of low production hives.
17N.2.sl.TZ0.8d.i: Find the value of \(k\);
17N.2.sl.TZ0.8d.ii: Find the number of hives that have a high production.
17N.2.sl.TZ0.8e: Adam decides to increase the number of bees in each low production hive. Research suggests that...
18M.2.sl.TZ1.8a: Find the value of a and of b.
18M.2.sl.TZ1.8b: Use the regression equation to estimate the value of y when x = 3.57.
18M.2.sl.TZ1.8c: The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0 , n ≠ 0 ,...
18M.2.sl.TZ2.1a.i: Find the value of a and of b.
18M.2.sl.TZ2.1a.ii: Write down the correlation coefficient.
18M.2.sl.TZ2.1b: Use your equation to estimate the mean weight of a child that is 1.95 years old.

Equation of the regression line of \(y\) on \(x\).

SPNone.2.sl.TZ0.8a: Write down the equation of the regression line of y on x .
SPNone.2.sl.TZ0.8b(i) and (ii): Use your regression line from part (a) as a model to answer the following. Interpret the meaning...
SPNone.2.sl.TZ0.8c: Estimate the cost of producing 60 boxes.
SPNone.2.sl.TZ0.8d: The factory sells the boxes for $19.99 each. Find the least number of boxes that the factory...
SPNone.2.sl.TZ0.8e(i) and (ii): Comment on the appropriateness of using your model to (i) estimate the cost of producing...
14M.2.sl.TZ1.3a(i): The relationship between the variables is modelled by the regression equation \(y = ax +...
14M.2.sl.TZ1.3a(ii): The relationship between the variables is modelled by the regression equation \(y = ax +...
14M.2.sl.TZ2.3a(i): Write down the value of \(a\) and of \(b\).
14M.2.sl.TZ2.3a(ii): Explain what the gradient \(a\) represents.
14M.2.sl.TZ2.3b: Use the model to estimate the amount of fuel the car would use if it is driven \(110\) km.
14N.2.sl.TZ0.2b: The relationship can be modelled by the regression line with equation \(y = ax + b\). Write down...
15M.2.sl.TZ1.1a: (i) Find the correlation coefficient. (ii) Write down the value of \(a\) and of \(b\).
15M.2.sl.TZ2.3a: (i) Find the value of \(a\) and of \(b\). (ii) Write down the value of \(r\).
15N.2.sl.TZ0.9b: Use the regression equation to estimate the number of coyotes in the reserve when \(t = 7\).
16M.2.sl.TZ2.8a: (i) Find the correlation coefficient. (ii) Write down the value of \(a\) and of \(b\).
16M.2.sl.TZ2.8b: Use the regression equation to estimate the price of Lina’s car, giving your answer to the...
16M.2.sl.TZ2.8c: Calculate the price of Lina’s car after 6 years.
16M.2.sl.TZ2.8d: Find the year when Lina sells her car.
17N.2.sl.TZ0.8a: Write down the value of \(a\) and of \(b\).
17N.2.sl.TZ0.8b: Use this regression line to estimate the monthly honey production from a hive that has 270 bees.
17N.2.sl.TZ0.8c: Write down the number of low production hives.
17N.2.sl.TZ0.8d.i: Find the value of \(k\);
17N.2.sl.TZ0.8d.ii: Find the number of hives that have a high production.
17N.2.sl.TZ0.8e: Adam decides to increase the number of bees in each low production hive. Research suggests that...
18M.2.sl.TZ1.8a: Find the value of a and of b.
18M.2.sl.TZ1.8b: Use the regression equation to estimate the value of y when x = 3.57.
18M.2.sl.TZ1.8c: The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0 , n ≠ 0 ,...
18M.2.sl.TZ2.1a.i: Find the value of a and of b.
18M.2.sl.TZ2.1a.ii: Write down the correlation coefficient.
18M.2.sl.TZ2.1b: Use your equation to estimate the mean weight of a child that is 1.95 years old.

Use of the equation for prediction purposes.

SPNone.2.sl.TZ0.8c: Estimate the cost of producing 60 boxes.
SPNone.2.sl.TZ0.8d: The factory sells the boxes for $19.99 each. Find the least number of boxes that the factory...
SPNone.2.sl.TZ0.8e(i) and (ii): Comment on the appropriateness of using your model to (i) estimate the cost of producing...
14M.2.sl.TZ1.3a(ii): The relationship between the variables is modelled by the regression equation \(y = ax +...
14M.2.sl.TZ2.3b: Use the model to estimate the amount of fuel the car would use if it is driven \(110\) km.
14N.2.sl.TZ0.2c: Rita scored a total of \(26\) in her IB Diploma. Use your regression line to estimate Rita’s...
15M.2.sl.TZ1.1b: Elizabeth watches television for an average of \(3.7\) hours per day. Use your regression line...
18M.2.sl.TZ1.8a: Find the value of a and of b.
18M.2.sl.TZ1.8b: Use the regression equation to estimate the value of y when x = 3.57.
18M.2.sl.TZ1.8c: The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0 , n ≠ 0 ,...

Mathematical and contextual interpretation.

SPNone.2.sl.TZ0.8b(i) and (ii): Use your regression line from part (a) as a model to answer the following. Interpret the meaning...
14M.2.sl.TZ2.3a(ii): Explain what the gradient \(a\) represents.
14N.2.sl.TZ0.2c: Rita scored a total of \(26\) in her IB Diploma. Use your regression line to estimate Rita’s...
15N.2.sl.TZ0.9b: Use the regression equation to estimate the number of coyotes in the reserve when \(t = 7\).
18M.2.sl.TZ1.8a: Find the value of a and of b.
18M.2.sl.TZ1.8b: Use the regression equation to estimate the value of y when x = 3.57.
18M.2.sl.TZ1.8c: The relationship between x and y can be modelled using the formula y = kxn, where k ≠ 0 , n ≠ 0 ,...