x y A random sample of two variables, x and y produced the following observations: 17 8 19 7 13 9 9 11 12 9 25 6 20 7 3. Test the significance of the slope of the correction model at a = 0.05 17 8 1. Develop a scatter plot of the data. Does the plot suggest a linear or nonlinear relationship betw dependent and independent variables? 2. Compute the correlation coefficient between x and y (to.05 1.9432)
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- For a data set of chest sizes (distance around chest in inches) and weights (pounds) of eight anesthetized bears that were measured, the linear correlation coefficient is r = 0.996. Use the table available below to find the critical values of Ⓡ r. Number of Pairs of Data n 4 5 6 7 8 9 10 11 12 OA.-0.707 OB. +0.707 OC.-0.707, +0.707 OD. +0.754 Critical Value of r 0.950 0.878 0.811 0.754 0.707 0.666 0.632 0.602 0.576Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant negative linear correlation between advertising cost and profit . Use a significance level of 0.01 and round all values to 4 decimal places. Advertising Cost Profit 17 4 15 20 6. 28 7 17 8 29 Ho: p = 0 На: р < 0 Find the Linear Correlation Coefficient r = Find the p-value p-value = The p-value is Less than (or equal to) a O Greater than a The p-value leads to a decision to Ассept Ho Reject Ho O Do Not Reject Ho The conclusion is O There is a significant negative linear correlation between advertising expense and profit. There is a significant positive linear correlation between advertising expense and profit. O There is a significant linear correlation between advertising expense and profit. O There is insufficient evidence to make a conclusion about the linear correlation between advertising expense and profit.A departmental store has the following sales for a period of last one year of 8 salesmen, who have different years of education. Years of Education 8 10 10 12 14 16 Annual Sales (Thousand Tk.) 100 120 80 100 80 100 70 130 a. Determine the correlation coefficient r between the two variables. Answer rounded to at least 4 decimal places. b. Determine the slope coefficient B1 for the regression of annual sales on years of education. Answer rounded to at least 4 decimal places. c. Determine the y-intercept Bo for the regression of annual sales on years of education. Answer rounded to at least 4 decimal places. d. What will be the annual sales when the years of education is 11 (years)? Answer rounded to at least 4 decimal places. Thousand Tk.
- The following zero order correlation coefficients are given : r12 = 0.5 r13 = 0.6 r23 =.7 %3D Calculate the multiple correlation coefficients R1,23, R2.13 and R3.12Listed below are the overhead widths (in cm) of seals measured from photographs and the weights (in kg) of the seals. Construct a scatterplot, find the value of the linear correlation coefficient r, and find the critical values of r using a = 0.05, Is there sufficient evidence to conclude that there is a linear correlation between overhead widths of seals from photographs and the weights of the seals? Overhead Width 7.1 7.5 178 Click here to view a table of critical values for the correlation coefficient. 9.6 9.4 8.8 8.2 Weight 112 205 238 204 188 OA. YB. OC. KD D. Aweight (kg) 300- A weight (kg) Aweight (kg) 300- Aweight (kg) 300- 300- .. 100 100+ 100 7. rect: 0 10 10 10 10 width (om) width (cm) width (on) widn (om) The linear correlation coefficient is r= (Round to three decimal places as needed.) Enter your answer in the answer box and then click Check Answer. O parts remaining Check Answer वीQ3: From the following data: 2 5 y 5 4 6 3 1) Draw scatter plot. 2) Determine the regression line y = a + b x. 3) Predict the value of y for the value of x = 4.6. 4) Calculate the correlation coefficient. 4 8 3 5
- Listed below are paired data consisting of amounts spent on advertising (in millions of dollars) and the profits (in millions of dollars). Determine if there is a significant linear correlation between advertising cost and profit Use a significance level of 0.01 and round all values to 4 decimal places. Advertising Cost Profit 3 21 4 16 5 29 17 7 28 8 21 Ho: p = 0 Ha: p +0 Find the Linear Correlation Coefficient r= Find the p-value p-value = The p-value is Less than (or equal to) a OGreater than a The p-value leads to a decision to Do Not Reject Ho OReject Ho OAccept HoThe data obtained in a study on the number of absences in virtual class and the final grades of seven randomly selected students from a mathematics class. The data are shown below. To determine the significance of the correlation coefficient at 0.05 level of significance, what is the calculated or computed value (CV)? Final grade y Number of absences x in a virtual class 6. 82 86 15 43 9. 74 58 5 90 78 а. -1.59 b. -2.32 с. 2.32 d. 1.59use the scatterplot to find the value of the rank correlation coefficient rs and the critical values con sponding to a 0.05 significance level used to test the null hypothesis of ps= 0. Determine whether there is a correlation. Distance/Time Data for a Dropped Object
- The paired data below consists of heights and weights of 6 randomly selected adults. Find the linear correlation coefficient, the linear regression line, and predict the weight of a randomly selected person who is 1.69 meters tall. X Height (meters) 1.61 1.72 1.78 1.80 1.67 1.88 Y Weight (kg) 54 62 70 84 61 92Calculate Pearson's correlation coefficient using the following values: (image attached)1:49 AA O www-awn.aleks.com : d on the same scale from a population, O REGRESSION AND CORRELATION Linear relationship and the.. y u V 1.0 3.0 1.0 7.2 11 10 10 9- 84 2.0 | 4.4 2.0 9.0 3.0 | 3.0 3.0 | 7.0 4.0 4.9 4.0 5.6 6- 5.0 4.3 5.0 8.1 4. 4- 6.0 | 7.0 6.0 4.8 2. 7.0 | 6.1 7.0 4.3 8.0 7.8 8.0 | 7.1 9.0 | 7.0 Figure 1 9.0 6.0 Figure 2 10.0 8.3 10.0 4.3 t mn w 1.0 10.0 1 10- x 9- 1.0 3.8 11 2.0 | 5.8 10- 94 2.0 9.0 3.0 | 8.1 3.0 | 8.0 7 4.0 7.0 4.0 | 9.2 6- 5. 5.0 10.3 4. 5.0 6.0 4- 3 3 6.0 9.7 6.0 5.0 2. 7.0 | 9.8 7.0 | 4.0 8.0 | 7.9 8.0 3.0 9.0 2.0 Figure 4 |10.0 1.0 9.0 | 6.6 Figure 3 10.0 3.7 Answer the following questions. The same response answer for more than one question. 1. Which data set has an apparent negative, but not perfect, linear relationship between its two variables? Choose one 2. In which data set is there evidence of a strong nonlinear relationship between the two variables? Choose one 3. Which data set indicates the strongest negative linear Choose one relationship…