Question

How much should a healthy Shetland pony weigh? Let x be the age of the pony (in months), and let y be the average weight of the pony (in kilograms). x 3 6 12 20 26 y 60 95 140 154 183 (a) Make a scatter diagram of the data and visualize the line you think best fits the data.

(b) Would you say the correlation is low, moderate, or strong? low moderate strong Would you say the correlation is positive or negative? positive negative

(c) Use a calculator to verify that Σ(x) = 67, Σ(x2) = 1265, Σ(y) = 632, Σ(y2) = 89,430, and Σ(x y) = 10,268. Compute r. (Enter a number. Round your answer to three decimal places.)

(d) As x increases from 3 to 26 months, does the value of r imply that y should tend to increase or decrease? Explain your answer. Given our value of r, y should tend to remain constant as x increases. Given our value of r, we can not draw any conclusions for the behavior of y as x increases. Given our value of r, y should tend to decrease as x increases. Given our value of r, y should tend to increase as x increases.

Answer 1

(a) To make a scatter plot in excel, enter the data column wise, select the data, click on Insert > Insert Scatter (X,Y) or Bubble Chart > Scatter BS. Book1 - Excel File Home Insert Page Layout Formulas Data Review View Help Tell me what you want to do Online Pictures + Screenshot Get Add-ins D Recommended a My Add-ins - PivotChart SmartArt Charts Shapes Pictures Pivot Table Recommended Table Pivot Tables Tables Map Illustrations Add-ins ChaTeatter JK Bubble 183 More Scatter Charts... Scatter plot 0 5 10 15 20 25 30

(b) From the scatterplot, if we visualize the line, all points closely follow the linear form. Hence, we can say there is a strong (strength) relationship between x and y. Scatter plot 1 10 15 20 25 30 *Line has been drawn manually to visualize and not obtained from excel Also, we can see the there is an increasing trend in points, as moving x increases, the y increases. Hence, the direction of the relationship is positive. (c) For calculating correlation coefficient r calculate x?, y2 and xy Ty x2 12 xx 3 60 9 3600 180 6 95 36 9025 570 12 140 144 19600 1680 20 154 400 23716 3080 26 183 676 33489 4758 67 632 1265 89430 10268 From the table, we have x = 67 Ey = 632 Ex2 = 1265 Ey2 = 89430 Exy = 10268 n = 5 (number of observations)

The correlation coefficient is given by, n(2xy) - (2x)(2y) r = = V[n{x2 – (Ex)2][n?y2 – (2y)2] 5 * 10268 – 67 * 632 V[5 * 1265 – 672][5 * 89430 – 6322] 8996 1836 * 47726 = 0.961 Note: we can calculate correlation coefficient using =CORREL function in excel (d) The general rule about the strength of relationship is Absolute Value ofr Strength of Relationship ir <0.3 None or very weak 0.3 < r <0.5 Weak 0.5 < 1r| <0.7 Moderate Ir >0.7 Strong Since, r is positive and lr| > 0.7, this proves that there is a strong positive linear relationship in x and y, which means as x increases, y will also increase. Hence, Given our value of r, y should tend to increase as x increases. Please rate the question if it was helpful, happy HomeworkLibing!