Ask Plex AI about problem 1
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Ask Plex AI about problem 1
Get hints, ask questions, and work through this problem step by step
Access custom-built, exam-style problems for -----------. Each problem has a full solution and mark-scheme, as well as AI grading and support.
Bivariate Statistics
Access custom-built, exam-style problems for Bivariate Statistics. Each problem has a full solution and mark-scheme, as well as AI grading and support.
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0 / 7
A teacher surveys his class to find out how long each student spent studying for a recent test. The time, in hours, each student spent studying is shown alongside their score in the following table.
Study time (h) | 0 | 1 | 2 | 4 | 5 | 8 |
|---|---|---|---|---|---|---|
Score (s) | 45 | 52 | 62 | 65 | 74 | 88 |
Find and interpret Pearson's product-moment correlation coefficient, r, for this data.
Find the equation of the regression line of s on t.
Use the regression line found in (b) to predict the score of a student who spent 7 hours studying.
Explain why the regression equation should not be used to predict the score of a student who studied 25 hours for the test.
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The resting body temperature, in degrees °C, of 6 adults is measured and recorded alongside their age, in years, in the table below.
Age (Y) | 41 | 46 | 49 | 51 | 55 | 61 |
|---|---|---|---|---|---|---|
Temperature (C) | 37.7 | 37.2 | 37.1 | 39.2 | 36.8 | 36.6 |
State the age of the outlier in this data set.
Suggest one reason the outlier identified in (a) should not be included in any further analysis.
The relationship between Y and C can be modelled by the equation C =aY+b.
Find the value of a and the value of b.
Find and interpret the value of Pearson's product-moment correlation coefficient, r, for these data.
Use the model C =aY+b to estimate the body temperature of a newborn, and explain why this is unlikely to be reliable.
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The following table shows the data collected in a study.
x | 1 | 2 | 4 | 5 | 6 | 8 |
|---|---|---|---|---|---|---|
y | 18 | 29 | 54 | 32 | 69 | 93 |
Write down the values of xˉ and yˉ.
Using the grid below, draw a scatter diagram for the data.
Hence state any outlier(s) in the data.
Plot a line of best fit on your scatter plot, and hence estimate the regression equation of y on x.
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Using your regression equation, predict the value of y when x=3.
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0 / 7
Perplex conducts a study on student performance in IB math. The scores of 5 students are shown in the following table alongside the number of mock exams each student completed.
Score (S) | 2 | 4 | 5 | 6 | 7 |
Number of mocks completed (N) | 4 | 3 | 7 | 10 | 9 |
The relationship between S and N can be modelled by the regression line N=aS+b.
Find the value of a and the value of b.
Write down the correlation coefficient for this regression, and interpret its significance.
Using the regression equation, predict the number of mock exams completed by a student who scored a 3.
Suggest two reasons why this model cannot reliably predict the score of a student who completed 0 mock exams.
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0 / 8
The government of Mongolia surveys 6 herding families living in the valley of Yolyn to find out how many goats and sheep each family owns.
Goats (g) | 17 | 33 | 46 | 79 | 93 | 114 |
Sheep (s) | 21 | 29 | 63 | 85 | 101 | 106 |
Find and interpret Pearson's product-moment correlation coefficient, r, for this data.
Find the equation of the regression line of s on g.
Use the regression line found in (b) to predict the number of goats (g) owned by a family in the valley with 205 sheep (s).
State two reasons why this prediction may not be accurate.
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0 / 6
A nutritionist records the amount of sugar (x, in grams) in ten different cereal brands and their average rating (y) given by a panel of tasters. The data are shown below.
x (grams of sugar) | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 | 22 |
|---|---|---|---|---|---|---|---|---|---|---|
y (taste rating) | 78 | 75 | 72 | 70 | 68 | 64 | 60 | 58 | 55 | 50 |
Use your calculator to calculate the Pearson product–moment correlation coefficient, r.
Describe the correlation between sugar content and taste rating.
Find the equation of the regression line of y on x, in the form y=mx+c.
Estimate the expected taste rating when a cereal contains 15 grams of sugar.
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0 / 6
A car manufacturer collects data on six of its petrol‑engine models, recording engine power x (in horsepower) and the corresponding average CO2 emissons y (in g/km):
Engine power x (hp) | 110 | 145 | 190 | 235 | 280 | 325 |
|---|---|---|---|---|---|---|
CO2 emissions y (in g/km) | 188 | 212 | 247 | 283 | 319 | 352 |
Use your graphic display calculator to find the equation of the regression line of y on x.
The engine power for the new prototype will be x=260hp.
Use your regression equation to estimate the CO2 emissions of the prototype.
The Pearson product–moment correlation coefficient is r=0.975, to three significant figures.
Explain why it is valid to use this regression model to make that estimate.
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0 / 7
Lucy operates a smoothie stall and has observed that warmer temperatures lead to higher sales of her smoothies. Over six days she recorded the maximum daily temperature, T(°C), and the number of smoothies sold, S. The results are:
T(°C) | 14 | 16 | 18 | 20 | 22 | 24 |
|---|---|---|---|---|---|---|
S sold | 118 | 132 | 140 | 155 | 165 | 158 |
The relationship between S and T is modeled by the regression line S=aT+b.
Find the values of a and b.
Write down the correlation coefficient r.
Using your regression equation, estimate the number of smoothies sold when T=21°C.
Interpret the value of the slope a in the context of the problem.