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HUMBEHV 3HB3 Lecture Notes - Lecture 10: Null Hypothesis, Scatter Plot, Standard Deviation

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11 Sep 2018

School

McMaster University

Department

Human Behaviour

Course

Professor

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Document Summary

In regression a steep slope means a high correlation: pearson r is not a good measure of regression slope, regression can answer several questions that correlation cannot. Where does the regression line come from: you want to ensure that preliminary analyses were done to ensure that there is nothing distorting the result. It minimizes the sum of the squared residuals, the least squares rule: the regression line always go through the point that is defined by the mean of the x value and the mean of the y. It is saying, what is the probability you will get an intercept that is that far from 0 just by this chance alone. In linear regression big r square is equal to little r square. In multiple regression this is not the same. If you set it to 0 the fit will get worse because it is not the best fitting line. Line is defined by intercepts and slope coefficient.

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Related Questions

ECON 3050

Q24. The coefficient of determination (r²) is calculated as 0.49, then the correlation coefficient:

Cannot be determined without the data

Should be - 0.70 or 0.70

Should be 0.

Neither of the above

Q25. A regression line is used for all of the following except one. Which one is not a valid use of a regression line?

To estimate the average value of Y at a specified value of X.

To predict the value of Y for an individual, given that individual's X-value.

To estimate the change in Y for a one-unit change in X.

To determine if a change in X causes a change in Y.

Q26. Which choice is not an appropriate description of YË in a regression equation?

Estimated response

Predicted response

Estimated average response

Observed response

Q27. Which of the following is the best way to determine whether or not there is a statistically significant linear relationship between two quantitative variables?

Compute a regression line from a sample and see if the sample slope is 0.

Compute the correlation coefficient and see if it is greater than 0.5 or less than â0.5.

Conduct a test of the null hypothesis that the population slope is 0.

Conduct a test of the null hypothesis that the population intercept is 0.

Q28. There is no relationship between variables unless the data points lie in a straight line.

True

False

Q29. The sample regression analysis

Is the same as the population regression line

Is used to estimate the population regression line

Shows the true relation between dependent and independent variables

None of the above.

Q30. In regression, a dependent variable is sometimes called a predictor variable.

True

False

Q31. In a linear regression equation of the form y = a + bx, the intercept shows

The amount that y changes when x changes by one unit

The amount that x changes when y changes by one unit

The value of y when x is zero

The value of x when y is zero.

Q32. In a linear regression equation of y = a + bx, the slope b shows

Y / b

X / b

Y / X

X / Y

yellowturtle964

Researchers measured the blood pressures of 22 students in

two situations: when the students were relaxed and when the students were taking an

important examination. The file

lists the systolic and diastolic pressures for

each student in each situation. Dataset is available at

systolic_url = "https://mcs.utm.utoronto.ca/~nosedal/data/systolic.txt"

to answer each of the following questions. You have to show

Answers, even if correct, with no justifications will not receive any

, compute the change in systolic pressure by subtracting systolic pressure when

relaxed from systolic pressure during the exam; call this variable

, repeat part a) for diastolic pressure. Call the resulting variable

, make a scatterplot of

, fit a regression line to the data and add

this line to your plot. Use: 2 c) your last name as the main title for your plot. (In my

case it would be: 2 c) Nosedal).

Important note. Use

as your response variable and label horizontal and vertical axes.

d) What is the fitted regression model? Provide slope and y-intercept

, make a residual plot from the regression in part c). Does this plot call into

question the use of a linear model? Why?

2 e) your last name

as the main title for your plot. (In my case it would

f) Note the outlier in the residual plot (and on the scatterplot from part c)).

, delete the outlier from the data set. Then repeat parts c) and e). Note. Use:

as the main title for your plots. (In my case it would be:

g) What is the fitted regression model (after the outlier has been removed)? Provide slope

and y-intercept

viridianleopard855

Topic: spectroscopy: examination of the absosorption spectrum and determination of the extinction coefficient for Flavin mononucleotide

2) in part 2 of the experiment, you are asked to prepare 5.0 mL of 2.0 x10-5M FMN starting with a 1.0 x 10 -4 solution of FMN? Calculate the amounts of 1.0 x 10-4 M FMN solution and water needed.

ice POT Il. Experimental Procedure 1) Examination of the absorption spectrum of FAIN. Prepare 5.0 mL of 1 x 10 4 MI FMN by luting 0 10 ml of 5.0 x 103 M FMN into 4.90 mL of water. Place about 3 mL in a plastic cuvette and take absorbance readings every 10 nm between 340 nm and 600 nm. (Use water as the blank and be sure to re-zero the blank every time you change the wavelength.) Tabulate the absorbance readings in Table l. Inspect the data and determine where the absorbance is maximal for use in the next part. Plot absorbance (y) vs. wavelength (x) in Excel. Be sure to label the axes correctly 2) Prepare 5 0 mL of 2.0 x 10-5 M FMN by diluting the 1.0 x 10-4 M FMN from part #1 appropriately. Place part of the new FMN sample you prepared in a quartz cuvette provided by the TA Collect an absorbance spectrum of the sample between 190 nm and 1100 nm using the Shimadzu UV1800. (Use water as your blank in the reference cuvette). Export your data to a thumb drive for later analysis in Excel. (Note- everyone in the lab must share the 4 Shimadzu spectrophotometers, so you may need to wait for your turn to complete this part. If so, proceed to parts 3 and 4 and return to this when one of the instruments is free.) 3) Construction of a calilbration curve. Prepare 4.0 mls of 5x104 M FMN by diluting the 5 x103 M FMN appropriately. Prepare 6 test tubes as indicated in the table below. Calculate the concentration of FMN present in each of the 6 tubes and enter concentrations in Table II. Set the wavelength on the Genesys to the wavelength where the absorbance of FMN is maximal in the visible region and measure the absorbance of each of the 6 test tubes. Record these values in Table II. (At the wavelength where the absorption is maximal we will get the greatest response and inaccuracies in setting the monochromator will be the smallest, since the slope of the absorbance spectrum at this point is the least.) Plot the absorbance vs, concentration in Excel. In Excel, add a linear regression trendline that goes through (0,0) and determine the slope of the line. This slope gives the extinction coefficient for the FMN under these conditions. Tube # 6 mL of 5x 104 M FMN0.1 02 04 0.6 0.8 1.0 4.9 48 4.644 42 4.0 mL of water 4) Determination of unknown. Dilute 1.0 mL of the FMN solution with unknown concentration into 4.0 ml of water. Measure the absorbance and record it in Table IlI Repeat this three times and average your results