ashcards","topicId":"ad660ba8-09e0-4a3d-85f2-5f5559413806","topicSlug":"straight-line-models","cards":[{"id":"121c29ea-7eb0-4b78-bacb-12b01952bb6d","cardType":"cloze","front":"A non-vertical straight line model has the form $\\text{[...]}$.","back":"A non-vertical straight line model has the form $\\boxed{y=mx+c}$.","points":null,"mcqOptions":null},{"id":"b8b60c32-7f00-4b56-9379-e83e832d1908","cardType":"cloze","front":"A straight line model assumes an approximately [ ].","back":"A straight line model assumes an approximately constant rate of change.","points":null,"mcqOptions":null},{"id":"afece814-9731-4761-9168-a1924b75b9cc","cardType":"cloze","front":"For points $(x_1,y_1)$ and $(x_2,y_2)$, the gradient is $\\text{[...]}$.","back":"For points $(x_1,y_1)$ and $(x_2,y_2)$, the gradient is $\\boxed{m=\\frac{y_2-y_1}{x_2-x_1}}$.","points":null,"mcqOptions":null},{"id":"d28de02f-fc3a-42ce-b3d2-d96e5cb2c33a","cardType":"basic","front":"If $x$ is measured in hours and $y$ in pounds, what are the units of $m$?","back":"Pounds per hour.","points":1,"mcqOptions":null},{"id":"86b90e40-38d7-41a4-a36d-b85e04cb504e","cardType":"basic","front":"What does a positive gradient predict as $x$ increases?","back":"The response variable $y$ increases.","points":1,"mcqOptions":null},{"id":"5e5b411d-f4dc-4147-baca-f154427919d4","cardType":"basic","front":"What does a negative gradient predict as $x$ increases?","back":"The response variable $y$ decreases.","points":1,"mcqOptions":null},{"id":"0a40658d-9419-47f1-b7ee-cb5d826dace9","cardType":"basic","front":"How should the gradient $m$ be interpreted in context?","back":"Each one-unit increase in $x$ predicts a change of $m$ units in $y$.","points":2,"mcqOptions":null},{"id":"6531e007-f6ca-459d-897e-2e22c14edb9b","cardType":"basic","front":"What does the intercept $c$ predict in a straight line model?","back":"The predicted value of $y$ when $x=0$.","points":1,"mcqOptions":null},{"id":"9978e378-8aa0-4776-8423-9a9d3a232efb","cardType":"basic","front":"Why might real observations not lie exactly on a straight line model?","back":"

Natural variation
Measurement error
Factors omitted from the model

","points":3,"mcqOptions":null},{"id":"7edf1470-7de7-4c27-84a4-ed92623f65c9","cardType":"cloze","front":"For gradient $m$ through $(x_1,y_1)$, point-gradient form is $\\text{[...]}$.","back":"For gradient $m$ through $(x_1,y_1)$, point-gradient form is $\\boxed{y-y_1=m(x-x_1)}$.","points":null,"mcqOptions":null},{"id":"982fc8f7-53e7-42d8-96ec-03880545d3ad","cardType":"basic","front":"How is $y=mx+c$ constructed from two known points?","back":"

Calculate $m$ from the two points.
Substitute one point to find $c$.

","points":3,"mcqOptions":null},{"id":"7a0b13a5-e827-4f08-a9b1-9fed946402b8","cardType":"basic","front":"A 2-hour bicycle hire costs £13 and a 5-hour hire costs £25. What is the model $C=mx+c$?","back":"$C=4x+5$.","points":3,"mcqOptions":null},{"id":"2c697fef-dc8e-4010-84d5-806ba3d95987","cardType":"basic","front":"How should a line of best fit be positioned?","back":"

Pass through the middle of the data.
Balance points above and below.

","points":3,"mcqOptions":null},{"id":"098b9438-20da-444e-8b35-2ef1abcd8ef3","cardType":"basic","front":"Why use two well-separated points on a line of best fit to calculate its gradient?","back":"It reduces the effect of graph-reading errors.","points":2,"mcqOptions":null},{"id":"b5f3219b-948c-4d25-9d9a-316a1ffb49ea","cardType":"cloze","front":"A residual is calculated using $\\text{[...]}$

1.5.8 Straight line models Flashcards

1.5.8 Straight line models Flashcards