Regression Calculation Write-Up

18. Draw a best-fit line for the Tonga Trench data. A best fit line is a smooth line that shows the trend of the data; the line does not have to pass through the data points.

The slope of the linear fit of the data is 1.0049. What this tells me about the water is that it is increasing at a close to constant rate – while my results were not completely accurate because the slope of the line was not one it was fairly close to the target

2. Compute the means for the following set of scores saved as Ch. 2 Data Set 3 using IBM® SPSS® software. Print out a copy of the output. (Please refer to attachment)

7.) Considering that the average number of home runs in 2001 was 2.092, and the model had predicted the average of 2.1564, I believe that is a fair prediction point overall. The residual for this point is -0.0644, which shows that our model is a good predictor of average home runs. This ties in with the answers I’ve discussed in question 4 and 5.

This equation is given to us on the AP formula sheet, so since Barons actually teaches you how to use this specific formula it makes it much easier to understand and was very helpful on the AP Exam. Another topic the Brase text did not cover very thoroughly was the Least Squares Line. Brase simply defines the line as, “The least-squares line devolved with x as the explanatory variable and y as the response variable can be used only to predict y values from specific x values. Baron 's on the other hand goes into detail in explaining how to find the line, its slope, and the standard deviation. It gives the equation ŷ=y + b1 (x-x). It also goes onto define ß as the slope of the true regression line, which can be found using a t score with degrees of freedom n-2. The equation for standard deviation is the sum of the squared residuals divided by the sum of the squared deviations of the mean.

There are 2 data points intersecting the deceleration curve. Most of the points are slightly below and above to the line of best fit. There are some data points that are slightly touching the line of best fit. All the points are scattered, except for 3 identical consecutive points around 17-18mins. Figure 1b has three-deceleration curve and one flat line. The deceleration curve containing the purple triangles represents 2.0mL of polyphenol-oxidase. All the points plotted for this deceleration curve are scattered throughout the line of best fit, except for 3 similar consecutive points at 18-19minutes. Although the points are scattered, there are some data points that are slightly touching the line of best fit, some are slightly above and below the line of best fit. There are only two data points that are intersecting the line of best fit. The second deceleration curve contains a set of data points that are represented by orange circles. These data points represent 1.5ml of polyphenol oxidase. There are two data points that are intersecting the line of best fit and two data points that are slightly touching the line of best

The causes for this trend in the graphs is because as the age or the mileage of a car increases the price decreases.. The age graph had the points more distributed while the mileage had them more clustered. The least-squares regression line also was closer in vicinity in the age graph than the mileage graph. This means that it fit the age graph better than mileage. The residual plots also told quite a bit of information. Neither one had a point too high or low or had any visible pattern meaning that a linear model would be appropriate. The plot with mileage had more points touching the line at zero. However, the plot with age had more points in total nearer the line of zero. The residual plots showed that more points for the age were nearer meaning that it would be more capable of prediction compared to the mileage even though it did have more points touching the line. Graphing was a great visual representation, but the statistics are where the math came into play and explained our findings in greater

values to calculate the slope. From the images of the dataset provided in the article, they only

The standard deviation of the UCS values per unit is for most units considerably higher than the standard deviation for the estimated strength value per unit (Fig. 5(d)). It is assumed that a unit has a characteristic strength distribution with a characteristic mean strength value, which is very likely for the

This experiment was performed to understand the process of linear least-squared analysis as well as developing the skills to use EXCEL and having the criteria for the best line of fit to ones’ graphs. Linear least-squared analysis is a statistical method to determine a line of best fit by minimizing the sum of squares created by a mathematical function. A “square” is determined by squaring the distance between a data point and the regression line. For the 1st order kinetics graph, the y-axis was for the sum of ln(A). The straight line equation came out to be y=-0.0224x-0.546 while the regression line was at a 0.99564 which was very good. For the 2nd order kinetics graph, the y-axis was for the sum of 1/A. The straight line equation came out to be y=0.0575x+1.6104 while the regression line was at a 0.97327 which was also quite good. Each data set had 9 degrees of freedom. The F-value for the first graph was 2057.16 and the 2nd graph was 327.67.

The original data plot shows a lot of noise and need to be smooth or reduce without interfering the data features. The 5, 7 and 9 point Moving Average is plotted using the whiskey data (See Figure 1.1, 1.2 and 1.3). After the Moving Average were applied it seems most of the noise were reduced in the plot and even though the peaks amplitude is different for each point of smoothing, the trend line and peaks is similar to each other (5,7 and 9 point).

The scatter plot of Credit balance ($) versus Size show that the slope of the 'best fit' line is upward (positive); this indicates that Credit balance varies directly with Size. As Size increases, Credit Balance also increases vice versa.

3. The slope of the linear regression line is 0.0647. This is shown in the equation of the line, on the right hand side of the chart.

The standard deviations Sx and Sy have been found using the following table of data:

In order to get a trend line (line of best fit) of the opening price and closing price of GOOGL, a scatter plot is created in sheet #4. The plot collects opening and closing price of GOOGL from 2014-09-01 to 2015-08-31, and will be able to predict what will be the closing price at a given opening price. The generated line of best fit has a R^2 value of 0.97682, which means accurate enough, and an equation of y = 0.9825x + 9.5443. With a slope less than one, the production indicates that in each possible opening price, the closing price would be a little bit lower, which might be a loss. Therefore, because of the possibility of loss, it fails the final trend