Use the table below to find the regression coefficients for b_0 and b_1. Explain what b_0 and b_1 represent Calculation of Regression Coefficients Beer (X) Cigarettes (Y) 8 16 6 13 2 4 4 9
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Use the table below to find the regression coefficients for b_0 and b_1. Explain what b_0 and b_1 represent
Calculation of Regression Coefficients
Beer (X) Cigarettes (Y)
8 16
6 13
2 4
4 9
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- Consider a regression model. The coefficient of determination (R2) gives the proportion of the variability in the dependent variable that is explained by the regression equation. True FalseA researcher is proposing that exercise makes a person more energized as a result they require less sleep. He carries out a survey on the number of hours of exercise per week and the average hours of sleep needed per night in order to feel well rested. The results are shown on page 2 for the 8 participants. Calculate and interpret the regression line for the data. Hours of exercise/week (x) Average hours of sleep needed/night (Y) 8.6 4 8.1 5.2 9 2 8.5 3.4 7.4 8 6.8 10 9.4 1.5 7.7 6Fourteen hikers were surveyed at Algonquin Park, and asked for how many days have you been hikingand far did your travel in that time? The equation for the linear regression line is y+3x + 10.3 where x is the number of days and y is the distance travelled. Does the data include an outlier? and if so which point? Number of days hiked 1 1 2 3 3 5 5 6 7 7 9 10 11 12 Distance Traveled (km) 12 17 18 19 21 23 25 23 30 31 37 39 41 52
- The data show the bug chirps per minute at different temperatures. Find the regression equation, letting the first variable be the independent (x) variable. Find the best predicted temperature for a time when a bug is chirping at the rate of 3000 chirps per minute. Use a significance level of 0.05. What is wrong with this predicted value? Chirps in 1 min Temperature (°F) 786 1091 1135 828 849 1092 64.5 85 82.4 68.5 75.2 87.5 What is the regression equation? y = + X (Round the x-coefficient to four decimal places as needed. Round the constant to two decimal places as needed.)Please help asapLast years Data Management class decided to see if there was a relationship between the score (out of 10) a student got on the two-variable stats quiz, and their score (out of 30) on the unit test. Use the given data to Quiz Score Test Score 6 8 10 9 10 20 26 29 26 30 a) Calculate the correlation coefficient. b) Perform a linear regression.
- Bluereef real estate agent wants to form a relationship between the prices of houses, how many bedrooms, House size in sq ft and Lot Size in sq ft. The data pertaining to 100 houses were processed using MINITAB and the following is an extract of the output obtained: The regression equation is Price = B + OBedroom + yHouse Size + ALot Size Coef SE Coef Predictor T Constant 37718 14177 2.66 ** Bedrooms 2306 6994 0.33 0.742 House Size 74.3 52.98 0.164 Lot Size -4.36 17.02 -0.26 0.798 R-Sq=56.0% R-Sq (adj)=54.6% S= 25023 Source DF MS F P Regression 3 76501718347 25500572782 *** **** Residual Error 96 60109046053 626135896 Total 99 a) Write out the regression equation. b) Fill in the missing values *, **, c) Use the p-value approach to determine if ø is significant at the 5% significance level and d) Is y significantly different from -0.5? e) Perform the F test at the 1% level, making sure to state the null and alternative hypotheses. f) Give an interpretation to the term "R-sq" and comment…Write a short note on regression analysisThe data show the chest size and weight of several bears. Find the regression equation, letting chest size be the independent (x) variable. Then find the best predicted weight of a bear with a chest size of 58 inches. Is the result close to the actual weight of 572 pounds? Use a significance level of 0.05. Chest size (inches) 46 57 53 41 40 40 Weight (pounds) 384 580 542 358 306 320 LOADING... Click the icon to view the critical values of the Pearson correlation coefficient r. What is the regression equation? y=nothing+nothingx (Round to one decimal place as needed.)
- Bluereef real estate agent wants to form a relationship between the prices of houses, how many bedrooms, House size in sq ft and Lot Size in sq ft. The data pertaining to 100 houses were processed using MINITAB and the following is an extract of the output obtained: The regression equation is Price = B + Bedroom + yHouse Size + ALot Size Predictor Coef SE Coef T P Constant 37718 2.66 ** Bedrooms 2306 0.33 74.3 -4.36 House Size Lot Size S-25023 Error Total R-Sq-56.0 % 96 99 14177 6994 52.98 17.02 0.742 0.164 -0.26 0.798 Source DE SS MS F Regression 3 76501718347 25500572782 *** Residual 60109046053 626135896 R-Sq (adj) -54.6% P d) Is y significantly different from -0.5? e) Perform the F test at the 1% level, making sure to state the null and alternative hypoteses. f) Give an interpretation to the term “R-sq” and comment on its value.How can the coefficient of determination be interpreted?A real estate analyst has developed a multiple regression line, y = 60 + 0.068 x1 – 2.5 x2, to predict y = the market price of a home (in $1,000s), using independent variables, x1 = the total number of square feet of living space, and x2 = the age of the house in years. The regression coefficient of x2 suggests this: __________. If the square feet area of living space is kept constant, a 1 year increase in the age of the homes will result in a predicted drop of $2500 in the price of the homes If the square feet area of living space is kept constant, a 1 year increase in the age of the homes will result in a predicted increase of $2500 in the price of the homes Whatever be the square feet area of the living space, a 1 year increase in the age of the homes will result in a predicted increase of $2500 in the price of the homes Whatever be the square feet area of the living space, a 1 year increase in the age of the homes will result in a predicted drop of $2500 in the price of the homes