Explain the basic idea of the relationship between the variables.

1. The title page
This linear regression report should have a title page. I am not too picky about format for the title page.
MLA Title Page Format
2. Abstract
Directly following the title page. It is fine to simply write “Abstract” at the top of the page then give the abstract as a paragraph below. Follow the link below for some guideline on how to write a good abstract –
Abstract
3. The introduction
In the introduction you explain the basic idea of the relationship between the variables. This part usually requires some research. You need, for example, to explain what the explanatory variable and the response variable are and why it they may be linearly related. Additionally, there needs to be an explanation as to whether one should expect the correlation to be either positive or negative and what this means in terms of the variables being analyzed. The introduction should culminate in a statistical hypothesis about beta, the true slope of the best fit line, stated as a formal statistical hypothesis. The introduction should start broad and narrow to the theory. Ideally, the first few sentences should attempt to “hook” the reader and compel them to read further.
4. Results section
In this section you give the scatterplots of the original data as well as the residual plot. Relevant statistics such as the p-value and coefficient of determination must be explained and interpreted in this section. Explain what the pattern in the scatterplot reveals about possible relationships between the variables.
5. Discussion section
In this part of the essay you explain how all the pieces of the puzzle fit together. Or if there are pieces that don’t fit, a pattern in the residual plot perhaps, then you explain how and why they don’t fit and what the implications are from the piece not fitting.
6. The conclusion
Is there a statistically significant relationship between the explanatory and response variables? Is the model useful for predicting values of the response variable? Are there limitations? The conclusion is where you, as the statistician, give your interpretation and opinion about what the data is revealing and what reasonable statistical conclusions could be drawn.
You may seek help and guidance from your classmates and any books or other resources, but the final write-up of your analysis (especially conclusions) must be in your own words. If I receive two or more write ups that are too similar, they will receive no credit.
7. The Variables and Data
Alluvial Aquifers
The current drought conditions in California makes an analysis regarding how well a new well might yield water is quite apropos. There are many variables that can effect how much water a well might produce. One variable is the type of material that allows the gaps and space for the water to exist within. In this case the data are from wells drilled into an alluvial aquifer. A first step to this analysis is to do a bit of research on what an alluvial aquifer is and what type of structure makes the space available for water storage. Notice that the grain size is one of the variables in this analysis. This is real world data and as such, there will be considerable variation and also numerous confounding variables. This is more the norm rather than the exception when working with real world data.
Data
Bedinger (1961) reported the median grain size of sand (in mm) in 59 alluvial aquifers in the Arkansas River Valley. The yield of each aquifer (in gal/day/ft2) was also reported. These data are given in the accompanying table.
Grain Size Yield
0.062 12
0.068 14
0.110 29
0.110 37
0.120 19
0.120 84
0.140 105
0.150 81
0.160 75
0.160 120
0.170 100
0.180 71
0.190 31
0.190 160
0.190 260
0.200 50
0.210 37
0.210 60
0.220 55
0.230 31
0.240 87
0.240 170
0.250 180
0.260 130
0.260 145
0.270 37
0.270 200
0.280 76
0.280 160
0.290 198
0.290 420
0.300 89
0.300 330
0.320 120
0.320 270
0.370 150
0.370 380
0.380 205
0.390 240
0.400 260
0.400 370
0.420 405
0.420 580
0.430 560
0.440 570
0.450 330
0.470 410
0.470 670
0.480 200
0.490 580
0.500 860
0.550 680
0.600 12
0.600 250
0.630 260
0.740 400
0.940 550
0.950 500

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