Math topic中文

Linear regression and least squares

Concepts of linear regression and method of least squares to find the equation of the regression line.

Practice questions

  1. 1A teacher conducts a survey on 7 students to investigate the relationship between the number of hours (hh) of "screen-t…
  2. 2The number of years (xx) an employee has worked for the company and the corresponding salary increment, in dollars (yy…
  3. 3It is believed that the probability pp of a randomly chosen pregnant woman giving birth to a Down's Syndrome child is r…
  4. 4In an experiment, the time taken, TT minutes, for a 1-kg block of ice to melt completely under 7 pre-determined tempera…
  5. 5An electrical appliance supplier is investigating the potential impact of monthly advertisement expenditure, denoted as…
  6. 6A researcher is investigating the relationship between the students' test marks and their average daily duration of slee…
  7. 7A small cafe sells one type of coffee. The selling price of a cup of coffee is reviewed and adjusted at the beginning of…
  8. 8In an experiment involving two chemicals xx and yy, a researcher recorded observations of values of yy for controlled…
  9. 9Data is gathered on how exam scores, y, vary with the number of hours, x, students spent studying for Mathematics each w…
  10. 10In a chemical reaction, a chemical mixture is left to cool down to room temperature. The temperature of the chemical mix…
  11. 11已知回归直线y=ax+by=ax+b斜率的估计值为1.231. 23，样本点的中心为点(4,5)(4,5)，当 x=2x=2时，估计 yy 的值为 ()() A. 6.466. 46 B. 7.467. 46 C. 2.542. 54…
  12. 12The shear strength of soil is the ability of the soil to resist tensional stresses and sustain loads. The water content…
  13. 13The probability of obtaining a head when a particular coin is tossed is pp. A fair cubical die has the number '1' on on…
  14. 14An experiment was conducted with a ramp placed on top of a table. A ball is then released from the ramp, at a height HH…
  15. 15The table below gives the world record time, in seconds, for the 100 metre race for the various years. | Year, xx | 199…
  16. 16Scientists are studying the growth of a particular species of bamboo. They want to understand how the height of the bamb…
  17. 17The average trade-in value, y thousand dollars, of a particular make of used car depreciates with the age of the car, x…
  18. 18A teacher conducts a survey on 7 students to investigate the relationship between the number of hours (hh) of "screen-t…
  19. 19Sharron who is an amateur swimmer has been attending swimming lessons. She records her time taken to swim 50 metres each…
  20. 20The table below gives the age in months kk and the diameter in cm hh of coconuts. | Age in month (k) | 1 | 2 | 3.5 | 4…
  21. 21A teacher conducts a survey on 7 students to investigate the relationship between the number of hours (hh) of "screen-t…
  22. 22The Department of Environmental Health did a research on how the number of mosquitoes, x, in a container varies with tim…
  23. 23A group of scientists is interested to find out the correlation between the number of species and the size of the natura…
  24. 24设有一个回归方程为 y∧=2−2.5x \overset{\land }{y}=2-2.5x，则变量xx增加一个单位时()() A. yy平均增加2.52.5个单位 B. yy平均增加22个单位 C. yy平均减少…
  25. 25An old film roll is treated with a chemical in order to improve the contrast. The table below shows the amount of chemic…
  26. 26A factory manufactures a certain product for sale. The following table gives the quantity of product manufactured, x uni…
  27. 27设回归直线方程为y^=2.5−2x\hat{y}=2.5-2x，当变量xx增加一个单位时，yy平均增加___ 个单位．
  28. 28The table gives the record time, tt seconds, for a particular 100-metre freestyle swimming long course event for women…
  29. 29A batch of plants is grown and then studied to examine how well they are growing. For each plant, data on two indicators…
  30. 30The yield per hectare, yy kg, of a crop is believed to depend on the average rainfall, xx mm, in the month of June. Fo…
  31. 31An experiment was carried out to test the effect of a new additive on the carbon emission of a petrol engine. The carbon…
  32. 32The following question has parts (a) and (b). The following scatter diagrams with 5 data points each have product moment…
  33. 33Research is being carried out into how the concentration of a drug in the bloodstream varies with time, measured from wh…
  34. 34In order to investigate whether there is a correlation between rainfall and crop yields, the total rainfall, xx mm, and…
  35. 35An energy company is studying the relationship between the average daily temperature, xx (in degrees Celsius), and the…
  36. 36Data is gathered on how exam scores, yy, vary with the number of hours, xx, students spent studying for Mathematics ea…
  37. 37The following scatter diagrams with 5 data points each have product moment correlation coefficients −0.7-0.7, 00, 11, no…
  38. 38A study was conducted on a group of pre-diabetic seniors to examine whether the number of hours of exercise per week (tt…