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The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, Y=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the
Price in dollars | 109 | 113 | 155 | 167 | 170 |
Number of Bids | 10 | 11 | 12 | 13 | 17 |
Summation Table
X | Y | XY | X2 | Y2 | |
BID 1 | 109 | 10 | 1090 | 11881 | 100 |
BID 2 | 113 | 11 | 1243 | 12769 | 121 |
BID 3 | 155 | 12 | 1860 | 24025 | 144 |
BID 4 | 167 | 13 | 2171 | 27889 | 169 |
BID 5 | 170 | 17 | 2890 | 28900 | 289 |
SUM | 714 | 63 | 9254 | 105464 | 823 |
Step 1: Find the estimated slope.
Step 2: Find the estimated y-intercept.
Step 3: Find the estimate value of y when x=113.
Step 4: Determine if the statement "All points predicted by the linear model fall on the same line" is true or false.
Step 5: Substitute the values you found in steps 1 and 2 into the equation for the regression line to find the estimated linear model. According to this model, if the value of the independent variable is increased by one unit, then find the change in the dependent variable y.
Step 6: Find the value of the coefficient of determination.
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- The table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, Y=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in dollars 31 38 42 44 46 Number of Bids 3 4 6 7 9 Summation Table X Y XY X2 Y2 BID 1 31 3 93 961 9 BID 2 38 4 152 1444 16 BID 3 42 6 252 1764 36 BID 4 44 7 308 1936 49 BID 5 46 9 414 2116 81 SUM 201 29 1219 8221 191 Step 1: Find the estimated slope. Step 2: Find the estimated y-intercept. Step 3: Determine the value of the dependent variable Y at x=0. Step 4: Find the estimate value of y when x=42. Step 5: Substitute the values you found in steps 1 and 2 into the equation for the…arrow_forwardThe table below gives the list price and the number of bids received for five randomly selected items sold through online auctions. Using this data, consider the equation of the regression line, yˆ=b0+b1x, for predicting the number of bids an item will receive based on the list price. Keep in mind, the correlation coefficient may or may not be statistically significant for the data given. Remember, in practice, it would not be appropriate to use the regression line to make a prediction if the correlation coefficient is not statistically significant. Price in Dollars 124 143 158 160 196 Number of Bids 12 13 15 16 20 Table Step 2 of 6 : Find the estimated y-intercept. Round your answer to three decimal places.arrow_forwardAn economist wants to determine whether there is a linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. The data are shown in the table below. c. Compute and interpret the correlation coefficient. d. Compute and interpret the coefficient of determination. e. Test for the significance of the linear relationship. Use a 0.05 level of significance. State your conclusion. Hint: Your conclusion is either of the following. • There is a significant linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. • There is no significant linear relationship between a country's gross domestic product (GDP) and carbon dioxide emissions. GDP 1.6 3.6 4.9 1.1 0.9 2.9 2.7 2.3 1.6 1.5 (trillion dollars) Carbon Dioxide Emissions 428.2 828.8 1214.2 444.6 264 415.3 571.8 454.9 358.7 573.5 (millions of metric tons)arrow_forward
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