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1、线性回归方程的教学设计（The teaching design of linear regression equation）Teaching target(1) by collecting the data of two related variables in the real problem, the scatter diagram is made, and the correlation between variables is intuitively understood by scatter diagram;(2) when the two variables have linear
2、 correlation, the linear line will be linear in the longer scatter point and will be linear backRegression equations are used to predict;(3) know the meaning of the least square method, and know the idea of least square method, can establish linear regression equation according to the linear regress
3、ion equation coefficient formula, and understand the definition of (linear) correlation coefficientTeaching emphasisThe drawing of scatter diagram and the method of solving the equation of regression lineTeaching difficultiesThe method of solving the equation of regression lineteaching processI. pro
4、blem situation1. situation:The objective things is most of the past studies on the relationship is a causal relationship, but in fact there were more of a non causal relationship for example: math and physics achievement of certain students, are linked to each other, but cannot think mathematics is
5、due, physics is the fruit, or conversely in fact mathematics and physics achievement is the fruit, but the real cause is the students learning ability and effort so that the functional relationship exists a deterministic relationship but there is also another non deterministic relationship relations
6、hip2. question:In order to find out the relationship between hot tea sales and temperature, a canteen was given a random table of the number of hot tea sold on a 6 day and the temperature of the day:Temperature / CTwenty-sixEighteenThirteenTenFourThe number of cupsTwentyTwenty-fourThirty-fourThirty-
7、eightFiftySixty-fourIf the temperature is one day, can you predict the cup number of hot tea sold by the canteen this day?Two student activitiesIn order to understand the general relationship between tea sales and temperature, we said the temperature in the abscissa and ordinate said sales of tea, t
8、he Cartesian coordinate system was established, the number of tables in the form of representation of the data points marked in the coordinate system in the future, we call such a graph as a scatter plot (scatterplot).As you can see from the right picture, these points are scattered near a straight
9、line, so you can use a linear function to approximate the relationship between hot tea sales and the temperatureWhat kind of straight line is chosen to approximate the relationship between hot tea sales and air temperature?We have a variety of thinking schemes:(1) select two points that can reflect
10、the change of a straight line, such as taking the straight lines of these two points;(2) take a straight line so that the number of points on one side of the line is almost the same as on the other;(3) take several sets of points, determine several linear equations, and then calculate the average of
11、 the slope and intercept of each line, as the slope and intercept of the line;.What kind of straight line is best?Three. Construct mathematics1. least square method:Fitting the points in a scatter plot with a straight line of equations, so that the line is closest to the point in the scatter plot. S
12、o, how do you measure the proximity of a line to six points in the diagram?We take the six values of the independent variables given in the table into the linear equation and obtain the corresponding six values:These six values should be as close as possible to the actual values in the table, so we
13、consider the sum of squares of deviations based on the idea of estimating the meanIs in line with the scatter in the vertical direction (vertical direction) on the square of the distance and so close to the degree, can be used to measure the six point line and map, trying to take the value of the mi
14、nimum. This method is called the least square method (also called least squares).The first is as constant, then a quadratic function. At that time, knowable, reached the minimum. Similarly, it is regarded as a constant, a quadratic function. At that time, reached the minimum. Therefore, at the time,
15、 the minimum value of the resulting solution.The linear equation was then, so when the temperature was up, hot tea sold for about a cup2. linear correlation:A linear relationship is called linear correlation, which can be approximated by a linear equation3. linear regression equation:Generally, ther
16、e are observation data as follows:.When the minimum value is obtained, it is called the linear regression equation fitting the data. The straight line represented by the equation is called the regression lineThis expression is unfolded, is a two degree polynomial, with the use of methods, can find t
17、he best value for the minimum value of the time.(*),Four. Mathematical applicationExample 1, a classmate opened a canteen, he studied the impact of temperature on hot drinks sales, statistics, obtained a sold hot drinks cup and the temperature of the day comparison table:Temperature / temperature-5Z
18、eroFourSevenTwelveFifteenNineteenTwenty-threeTwenty-sevenThirty-oneThirty-sixNumber of hot drinksOne hundred and fifty-sixOne hundred and fiftyOne hundred and thirty-twoOne hundred and twenty-eightOne hundred and thirtyOne hundred and sixteenOne hundred and fourEighty-nineNinety-threeSeventy-sixFift
19、y-four(1) draw a scatter plot;(2) the general law of the relationship between the temperature and the number of hot drinks sold from the scatter plots;(3) finding the regression equation;(4) if the temperature is 2 degrees a day, predict the number of hot drinks sold on that dayConclusion: (1) scatt
20、er diagram is shown below:(2) from the top view, the points are scattered from the upper left to the lower right. Therefore, there is a negative correlation between the temperature and the number of hot drinks sold, i.e., the higher the temperature, the less the number of hot drinks sold(3) from the
21、 scatter diagram, it can be seen that these points are approximately distributed in the vicinity of a straight line. Therefore, the coefficients of the regression equation can be derived by formula. The regression equation =-2.352x+147.767. can be easily obtained by using a calculator(4) when x=2, =
22、143.063., so when one days temperature is 2 degrees, about 143 hot drinks can be sold this dayThinking: when the temperature is 2 degrees, will the canteen be able to sell 143 or so hot drinks? Why?Case 2 below is the statistics of the number of motor vehicles and the number of traffic accidents in
23、a given area in recent yearsThe number of motor vehicles is x / 1000Ninety-fiveOne hundred and tenOne hundred and twelveOne hundred and twentyOne hundred and twenty-nineOne hundred and thirty-fiveOne hundred and fiftyOne hundred and eightyThe number of traffic accidents is Y / thousand piecesSix poi
24、nt twoSeven point fiveSeven point sevenEight point fiveEight point sevenNine point eightTen point twoThirteen(1) please judge whether there is a linear correlation between the number of motor vehicles and the number of traffic accidents, and if there is no linear correlation, explain the reasons;(2)
25、 if we have linear correlation, we can find the linear regression equationConclusion: (1) draw the scatter diagram of the data in the Cartesian coordinate system, as followsIntuitively, the scatter point is near a straight line, so it has linear correlation(2) calculate the sum of the corresponding
26、data:=1 031, =71.6, =137 835, =9, 611.7.They will be calculated into the formula: B = 0.0774, a=-1.024 1,So the linear regression equation is =0.077 4x-1.024 1.Five, class summary:1. linear regression analysis of a set of data, should draw the scatterplot, to see whether it is linear, then in accord
27、ance with the formula, the coefficient calculated. Due to the large amount of calculation, so the calculation should be through technical means, careful, beware of errors in the calculation. For linear regression equation the steps of calculating the average product; calculate; calculation; the results obtained by substituting formula; regression equation; write