Physician supply and preventable hospital stays across 48 counties are fitted with one line, and the HS345 Unit 9 regression exercise example explains why its slope is not a cause. Searches like "hs 345 unit 9 assignment example", "hs345 unit 9 sample" and "hs345 unit 9 example" land here.
What a finished HS345 Unit 9 regression exercise looks like
A scatter plot opens the exercise, with physicians per 100,000 on the horizontal axis and preventable stays per 100,000 enrollees on the vertical, rural counties drawn as open circles. The fitted equation appears beneath it: predicted stays equal 4,946 minus 16.5 times physician supply. A small table reports the slope with its standard error of 2.45 and a 95 percent interval of minus 21.4 to minus 11.6, the correlation of minus 0.70, and an R squared of 0.50. Two predictions follow, about 4,290 stays at 40 physicians and 3,300 at 100, each rounded because the residual standard deviation is near 420. A residual plot comes next, and then a second pair of lines, one fitted within rural counties and one within metropolitan counties.
How a HS345 Unit 9 example is structured
The exercise moves from picture to equation to doubt. The scatter plot comes first so that direction, form and scatter are judged by eye before any number is computed. Fitting and interpretation follow, with the slope put into words once: each additional ten physicians per 100,000 residents is associated with about 165 fewer preventable stays per 100,000 enrollees. Prediction is kept inside the observed range of 22 to 117 physicians, and the exercise says so. The residual plot then earns the turn: rural counties sit above the line on average by about 230 stays and metropolitan counties below it, a pattern a single line cannot absorb. Fitting within each group shrinks the slope to about minus 6 in both, with intervals that both include zero. What else differs between rural and metropolitan counties, including age, income and hospital distance, fills the final paragraph.
Direction, form, strength
The scatter is read before fitting: downward, roughly linear, moderately strong, with no single county dominating. Rural points cluster at the upper left.
One slope in words
Minus 16.5 stays per additional physician, restated per ten physicians so the figure describes a realistic change. The intercept lies outside the data and is left uninterpreted.
Half the variation, not all
An R squared of 0.50 means physician supply accounts for about half the county-to-county variation in stays. The remaining half is not assigned to any cause.
Residuals sorted by type of county
Plotting residuals with rural and metropolitan markers shows two bands. The line overpredicts metropolitan counties and underpredicts rural ones on average.
Two lines inside the one
Within metropolitan counties the slope is minus 5.6, interval minus 11.5 to 0.4; within rural counties minus 6.0, interval minus 19.3 to 7.3. Most of the overall slope lies between the groups.
Why the slope is not a cause
Counties are not people, physician supply travels with urban setting and income, and no county was assigned its physicians. The exercise states an association and stops there.
Where marks go in HS345 Unit 9
Credit on a regression exercise at this level is usually spread across four areas: describing the scatter plot, interpreting the slope and R squared in context, checking the model through residuals, and drawing a conclusion that stays within the evidence. Slope interpretation needs units on both sides and the word associated, not causes or reduces. R squared is often misread as the share of counties the line fits, or as the correlation itself, and either reading costs the row. Residual credit depends on plotting them and reading the pattern, which is where this exercise finds its rural and metropolitan split. Conclusion credit goes to the paragraph on confounding and county-level data. Deductions also follow predictions far outside the observed range, an interpreted intercept, and a physician recruitment recommendation presented as the analysis's finding.
Get a HS345 Unit 9 example written to your instructions
Regression prompts in HS345 Unit 9 vary in their data, from county measures to patient-level readings. Attach yours, or the output it produced, along with the instructions and rubric. Delivered within 24-48 hours, the first custom sample is free and interprets the slope in the data's own units, plots the residuals, and says plainly what the line cannot establish.
HS345 Unit 9 questions, answered
What does it mean that the data are ecological?
Each point is a county, not a person. A pattern across counties does not show that any individual patient with better physician access avoided a hospital stay. Individual-level data would be needed for that claim. The example flags this in its conclusion, because ecological associations can be stronger, weaker or even reversed at the individual level.
Why fit separate lines for rural and metropolitan counties?
Because the residual plot showed the two groups sitting on different sides of the single line, a sign that rural status is related to both variables. Fitting within each group is a simple way to see how much of the overall slope survives once that difference is held aside. Multiple regression, covered later in many courses, does the same job more formally.
Can I report the correlation instead of the slope?
Report both if the prompt allows. The correlation of minus 0.70 describes strength and direction without units, while the slope says how much stays change per physician, which is what a planner needs. Most regression rubrics expect the slope interpreted in context, so leaving it out usually costs more than leaving out the correlation.