I\'m looking for the answer in terms of numbers not just work. Using Regression

ID: 3171374 • Letter: I

Question

I'm looking for the answer in terms of numbers not just work.

Using Regression in Data Analysis of Excel, find the estimated regression equation for Interval from Duration. In Excel output identify the coefficient of determination. What is the interpretation of this coefficient? What is the estimated variance of the error term E in the assumed model y=B0 + B1x + E? What is the estimated standard deviation of the error term?

Using Excel output found, at the 5% significance level, conduct the t test for testing the significance of Duration; (Specify clearly your hypotheses, indicate the value of the test statistic and the distribution of the test statistic, find the test p-value, make your conclusion and interpret this conclusion.)

Duration Interval 216 79 108 54 200 74 137 62 272 85 173 55 282 88 216 85 117 51 261 85 110 54 235 84 252 78 105 47 282 83 130 52 105 62 288 84 96 52 255 79 108 51 100 47 207 78 184 69 272 74 216 83 118 55 245 76 231 78 266 79 258 73 268 77 202 66 242 80 230 74 121 52 112 48 290 80 110 59 287 90 261 80 113 58 274 84 105 58 272 73 199 83 230 64 126 53 278 82 120 59 288 75 283 90 110 54 290 80 104 54 293 83 223 71 100 64 274 77 259 81 134 59 270 84 105 48 288 82 109 60 264 92 250 78 282 78 124 65 282 73 242 82 118 56 270 79 240 71 119 62 304 76 121 60 274 78 233 76 216 83 248 75 260 82 246 70 158 65 244 73 296 88 237 76 271 80 130 48 240 86 132 60 260 90 112 50 289 78 110 63 258 72 280 84 225 75 112 51 294 82 149 62 262 88 126 49 270 83 243 81 112 47 282 84 107 52 291 86 221 81 284 75 294 89 265 79 102 69 278 81 139 50 276 85 109 51 265 87 157 63 244 67 255 77 118 56 276 88 226 81 270 82 136 55 279 90 112 45 250 83 168 56 260 89 110 46 263 82 113 51 296 86 122 53 224 79 254 81 134 69 272 82 289 77 260 76 119 59 278 80 121 49 306 96 108 53 302 77 240 77 144 65 276 81 214 71 244 70 270 81 245 93 108 53 238 89 132 45 249 86 120 58 230 78 210 66 275 76 142 63 300 88 116 52 277 93 115 49 125 57 275 77 200 68 250 81 260 81 270 73 145 50 240 85 250 74 113 55 275 77 255 83 226 83 122 51 266 78 246 84 110 46 265 83 131 55 288 81 110 57 288 76 245 84 238 77 254 81 210 87 262 77 135 51 280 78 126 60 261 82 248 91 112 53 276 78 107 46 262 77 231 84 116 49 270 83 143 71 282 80 112 49 230 75 205 64 254 76 144 53 288 94 120 55 249 76 112 50 256 82 105 54 269 75 240 78 247 79 245 78 256 78 235 70 273 79 245 70 145 54 251 86 133 50 267 90 113 54 111 54 257 77 237 79 140 64 249 75 141 47 296 86 174 63 275 85 230 82 125 57 262 82 128 67 261 74 132 54 267 83 214 73 270 73 249 88 229 80 235 71 267 83 120 56 257 79 286 78 272 84 111 58 255 83 119 43 135 60 285 75 247 81 129 46 265 90 109 46 268 74

Explanation / Answer

Solution:

Here, we have to develop the regression model for the prediction of the dependent variable interval based on the independent variable duration. The regression output by using Excel is given as below:

SUMMARY OUTPUT

Regression Statistics

Multiple R

0.896069714

R Square

0.802940933

Adjusted R Square

0.802205638

Standard Error

6.003549546

Observations

270

ANOVA

Significance F

Regression

39358.46647

1091.9983

1.62425E-96

Residual

268

9659.418716

36.04260715

Total

269

49017.88519

Coefficients

Standard Error

t Stat

P-value

Lower 95%

Upper 95%

Intercept

33.98780757

1.18121714

28.77354757

6.133E-84

31.66216216

36.31345298

Duration

0.176862935

0.00535212

33.04539787

1.624E-96

0.166325386

0.187400484

The correlation coefficient between the dependent variable interval and independent variable duration is given as 0.8961 which means there is a strong positive linear association or relationship exists between the dependent variable interval and independent variable duration. The coefficient of determination or the value of the R square is given as 0.8029 which means about 80.29% of the variation in the dependent variable interval is explained by the independent variable duration. The standard error for this regression model is given as 6.00. This regression model is based on the 270 values of the dependent and independent variables.

For this regression model, the p-value is given as 0.00 approximately which is less than the level of significance or alpha value 0.05. So, we reject the null hypothesis that there is no any statistically significant relationship or linear association exists between the dependent variable interval and independent variable duration. This means we conclude that there is sufficient evidence that there is a statistically significant relationship exists between the dependent variable interval and independent variable duration.

The y-intercept for the regression equation is given as 33.9878 and it is statistically significant because the p-value for the corresponding t test is given as 0.00 approximately which is less than the level of significance or alpha value 0.05. The coefficient of the variable duration or the slope for the regression equation is given as 0.1769 and this slope is statistically significant at the 5% level of significance because the p-value for the corresponding t test is given as 0.00 approximately. The required regression equation for the prediction of the interval based on the duration is given as below:

Interval = 33.9878 + 0.1769*Duration

By using this regression equation, we can predict the value of Interval based on the given duration.