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3. The table summarizes data for a [fictional ] study veggigdod stressophil of the relationship between the concentration of Means 63.40 29.70 hormone called stress...

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3. The table summarizes data for a [fictional ] study veggigdod stressophil of the relationship between the concentration of Means 63.40 29.70 hormone called stressophil in Ltg and the ingestion std: dev' $ S, = 10.0217 S,= 6.84564 of a food substance, veggigood in grams. The sample size. is 12 correlation T= 0.83055 a)[2] Calculate the slope of the regression line Coefficient using the appropriate formula involving the statistics given in the table just above. Hint: USE THE FORMULAS in se

3. The table summarizes data for a [fictional ] study veggigdod stressophil of the relationship between the concentration of Means 63.40 29.70 hormone called stressophil in Ltg and the ingestion std: dev' $ S, = 10.0217 S,= 6.84564 of a food substance, veggigood in grams. The sample size. is 12 correlation T= 0.83055 a)[2] Calculate the slope of the regression line Coefficient using the appropriate formula involving the statistics given in the table just above. Hint: USE THE FORMULAS in sec: 12.3 for the Least-Squares Regression Line; Round to 4 significant digits . b)[2] Calculate the intercept of the regression line, using the given statistics. Round to significant digits. c)[2] Write out the sample regression equation for the data symbolically using the coefficients you found above Yyix Now fill in the contextually-styled equation as seen in research articles, using the variable names in the table abov (This may sEEm trivial but the point is that bY mindfully dping; we Iearn ] e)[2] Interpret the slope in English, beginning An increase of gram of linearly associated with f)[2] Because the residual sum of squares for regression; SSRe sidtul (I-r2 SS;Otal and the sample variance. SSJQtA the residual sum of squares can be found as SS KESIDUAL (1-r )(n-1)s} Calculate SSRESIDUAL using the statistics given above: precise to decimal places. g)[2] Now; find the Residual Standard Deviation for the data , Se RESDUAL n -2 precise t0 six decimal places_



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Please do the following. (a) Draw a scatter diagram displaying the data. (b) Verify the given sums $\Sigma x, \Sigma y, \Sigma x^{2}, \Sigma y^{2},$ and $\Sigma x y$ and the value of the sample correlation coefficient $r$. (c) Find $\bar{x}, \bar{y}, a,$ and $b .$ Then find the equation of the least-squares line $\hat{y}=a+b x$. (d) Graph the least-squares line on your scatter diagram. Be sure to use the point $(\bar{x}, \bar{y})$ as one of the points on the line. (e) Interpretation Find the value of the coefficient of determination $r^{2} .$ What percentage of the variation in $y$ can be explained by the corresponding variation in $x$ and the least-squares line? What percentage is unexplained? Answers may vary slightly due to rounding. You are the foreman of the Bar-S cattle ranch in Colorado. A neighboring ranch has calves for sale, and you are going to buy some to add to the Bar-S herd. How much should a healthy calf weigh? Let $x$ be the age of the calf (in weeks), and let $y$ be the weight of the calf (in kilograms). The following information is based on data taken from The Merck Veterinary Manual (a reference used by many ranchers). $$\begin{array}{c|cccccc}\hline x & 1 & 3 & 10 & 16 & 26 & 36 \\\hline y & 42 & 50 & 75 & 100 &150& 200 \\\hline\end{array}$$ Complete parts (a) through (e), given $\Sigma x=92, \Sigma y=617, \Sigma x^{2}=2338, \Sigma y^{2}=82,389, \Sigma x y=13,642$ and $r \approx 0.998$. (f) The calves you want to buy are 12 weeks old. What does the least-squares line predict for a healthy weight?

This is problem number 20 We are given a set of data regarding the length of the bear and the bears weight and our tests to first find the least grocery Russian to do this, we will find our five key data points. So we have some vax is 1017. Some of Y685, some of X times y 96 90 some of X squared is 1 56 5 49. And the sum of Y squared is 60,875. So we use these points with our two equations for coefficients and we find our least squares regression line as white hat equal to 0.61 seven X zero 330 So for part B we can interpret this firstly. We cannot directly interpret the Y intercept since it is negative and having a length of zero does not make sense though we can in turn interpret our slope. This pretty much says that an increase in length corresponds with a smaller increase in weight, specifically one cm more of length is .617. With the unit for this, the unit is kg, so .617 kg increase per centimeter length increase. So we can then find The prediction for the weight of a bear that is 149 cm long. Using our equation for x equal to 149,000 we get a white hat Equal to 91 0.57 Based on our input data, we know that Our value of 149 for why gives us exactly 85. So because our residual is 657 and it's positive, we can say that this bear specifically is below average for weight.

What we are given the following data points X. Y. Listed at the top of this white board. And we want to use that answer information to answer the following six questions A through F. As follows. First in part A on the left, we want to produce a scatter plot of this data. We've already done so with the scattered provided right below and the data points marked with X's or crosses next. We want to compute the sums and the correlation coefficient are on the right. I've already listed the sums out their computers simply by following the formula sum of all X values, some of our Y values and so on. The correlation coefficient. R. Is given by this formula which makes use of the sample size and and the sounds we just computed, plugging in these values, we get articles 0.9 98. Next part C. We want to find the X. Meanwhile, I mean and the constant related to the equation line of best fit. So exciting. And what I mean are simply given as follows. Remember that the being a value they're given by the following formulas. He takes his input and the sums. It's very similar to the correlation coefficient are plugging in. We get the equals 4.509 and plugging in Wiebe R. E. And explode at a gives 33.696 Guest we have our equation for the line of best fit. White hot equals 33.6964 point 509 X. Next we want to plot this. Why had onto our scatter plot, Making sure to include our expire and are Y. Bar we do sell it as is observable here. Next let's calculate R squared and interpret so R squared to simply 0.9954 That means that approximately 99.54% of our data can be rather 99.54% of variations in our data can be explained to the data itself, and roughly half of a percent cannot be explained. Finally, for F we want to project Why, for X equals 12. Using Ry had equation. Doing so, we obtain 87.804.

Were given the set of data points listed at the top of this whiteboard X fly. And we want to use these data points to answer the following questions. A through F. Starting off with part A on the left, we want to produce a scatter plot of these data points. I've already included the scatter plot. As you can see where the data points X. Y are demarcated by the black crosses or exits next to the right and part B. We want to compute the sum is relevant to the state to as well as the Pearson correlation coefficient. R The sums are given by following the forms exactly. So some access to some of the X values. Some why is some of the individual Y values and so on. To compute are we use the following formula which takes us input, our sample size and and the Sun is just computed. This gives our equals .9126. Next below. In parts you want to find the equation of the line of best fit which requires finding these parameters first are simple mean X bar and a sample mean Y bar are given by the sum of our X values about it by n 6.25 And some of our Y values over M 32.8. Yeah, we can find the parameters for our best fit. Line being a. As follows. The slope B is given by the equation here, which takes us input and the sample size and the sums we found above Plugging In. We get the equal 22 and then plugging in. Ry bar be an X bar to our A equation on the right gives us intercept negative 104.7. This means we have equation for the line of best fit why hat equals negative 104.7 plus 22 X. Next part Do we want to return to the scatter plot on the left and graph ry hat. Doing so we want to make sure we include our X. Men and women, which looks like this next in the bottom right part. You want to calculate? The coefficient of determination are square and interpret its meaning. This is simply the square of the correlation coefficient 0.83 to eight. We interpret this to mean that roughly 83 of the variation of the data can be explained by the corresponding variation and excellently squares line 17 of the data accordingly cannot be explained by this. Finally, in part, after the bottom, we predict y where x equals 6.5 Plugging into our white hat, we obtain 38.3.


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