Exam 2: Data

The correlation between X and Y is r = 0.35. If we double each X value, decrease each Y by 0.20, and interchange the variables (put X on the Y-axis and vice versa), the new correlation

If the point in the upper left corner of the scatterplot is removed, what will happen to the correlation (r) and the slope of the line of best fit (b)?

In an effort to decide if there is an association between the year of a postal increase and the new postal rate for first class mail, the data were gathered from the United States Postal Service. In 1981, the United States Postal Service changed their rates on March 22 and November 1. This information is shown in the table below. Year Rate 1971 0.08 1974 0.10 1975 0.13 1978 0.15 1981 0.18 1981 0.20 1985 0.22 1988 0.25 1991 0.29 1995 0.32 -Do you think a linear model is appropriate here? Explain.

The bigger the stop sign, the more expensive it is. Here is a graph of the height of a sign in inches versus its cost in dollars. To achieve linearity, the data was transformed using a square root function of cost. Here are the results and a residual plot. Dependent Variable: $\operatorname{sqrt}(\cos t)$ $R$ (correlation coefficient) $=0.98946627$ $R-s q=0.97904349$ s: 0.2141 Parameter coeff se Intercept 1.1857 0.4346 height 0.1792 0.0151 -Interpret R-sq in the context of this problem.

Carbon dating QuarkNet, a project funded by the National Science Foundation and the U.S. Department of Energy, poses the following problem on its website:"Last year, deep within the Soudan mine, QuarkNet teachers began a long-term experiment to measure the amount of carbon-14 remaining in an initial 100-gram sample at 2000-year intervals. The experiment will be complete in the year 32001. Fortunately, a method for sending information backwards in time will be discovered in the year 29998, so, although the experiment is far from over, the results are in." \begin{array}{l|c|c|c|c|c|c|c|c|c|c} \text {Time (\mathrm{yr}) }& 0 & 2000 & 4000 & 6000 & 8000 & 10,000 & 12,000 & 14,000 & 16,000 & 18,000 \\\hline \text {Mass (g) }& 100 & 76 & 61 & 47 & 36 & 29 & 22 & 17 & 13 & 10\end{array} A scatterplot of the data looks like: a. Straighten the scatterplot by re-expressing these data and create an appropriate model for predicting the mass from the year. b. Use your model to estimate what the mass will be after 7500 years. c. Can you use your model to predict when 50 g of the sample will be left? Explain.

Medical records indicate that people with more education tend to live longer; the correlation is 0.48. The slope of the linear model that predicts lifespan from years of education suggests that on average People tend to live 0.8 extra years for each additional year of education they have. The slope of the line that would predict years of education from lifespan is

The bigger the stop sign, the more expensive it is. Here is a graph of the height of a sign in inches versus its cost in dollars. To achieve linearity, the data was transformed using a square root function of cost. Here are the results and a residual plot.Dependent Variable: sqrt(cost) $\mathrm{R}$ (correlation coefficient) $=0.98946627$ $R-s q=0.97904349$ s: 0.2141 Parameter coeff se Intercept 1.1857 0.4346 height 0.1792 0.0151 -Write the transformed regression equation. Make sure to define any variables used in your equation.

The price of first class stamp has followed inflation over time and has increased at a constant percentage over time. The most useful predictive model is probably……

Which statement about influential points is true? I. Removal of an influential point changes the regression line. II. Data points that are outliers in the horizontal direction are more likely to be influential than points that are outliers in the vertical direction. III. Influential points have large residuals.

After conducting a survey at a pet store to see what impact having a pet had on the condition of the yard, a news reporter stated "There appears to be a strong correlation between owning a pet and the condition of the yard." Comment on this observation.