Problem 3. (40 points) A random sample of 15 NBA players' heights and weights are being analyzed

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Problem 3. (40 points) A random sample of 15 NBA players' heights and weights are being analyzed. The data are recorded as follows: Player Height, x Weight, y x² xy 1 198 100 39204 19800 2 216 118 46656 25488 3 206 95 42436 19570 4 203 101 41209 20503 5 206 109 42436 22454 6 201 98 40401 19698 7 198 86 39204 17028 8 213 113 45369 24069 9 193 86 37249 16598 10 182 73 33124 13286 11 213 122 45369 25986 12 196 88 38416 17248 13 191 80 36481 15280 14 211 120 44521 25320 15 211 107 44521 22577 Column Sum 3038 1496 616596 304905 Column Average 202.53 99.73 Table 1: NBA height and weight analysis (a) (10 points) Estimate the linear regression line (Round to three decimal places). (b) (5 points) With the fitted linear regression line in part (a), estimate the mean weight when the height is 200, i.e., x = 200 (Round to three decimal places). (c) (5 points) Given SST = 3200.93 and SSE = 379.02, determine the proportion of variability explained by the fitted model, i.e., compute the coefficient of determination R². (d) (20 points) With the fitted linear regression line, the SSE is 379.02 and Sxx = 1299.73. Use t-statistic to test the hypothesis that H0 : ?1 = 3.0 against H1 : ?1 < 3.0. Use a 0.05 level of significance.

          Problem 3. (40 points) A random sample of 15 NBA players' heights and weights are being analyzed. The data are recorded as follows:

Player Height, x Weight, y x² xy
1 198 100 39204 19800
2 216 118 46656 25488
3 206 95 42436 19570
4 203 101 41209 20503
5 206 109 42436 22454
6 201 98 40401 19698
7 198 86 39204 17028
8 213 113 45369 24069
9 193 86 37249 16598
10 182 73 33124 13286
11 213 122 45369 25986
12 196 88 38416 17248
13 191 80 36481 15280
14 211 120 44521 25320
15 211 107 44521 22577
Column Sum 3038 1496 616596 304905
Column Average 202.53 99.73

Table 1: NBA height and weight analysis

(a) (10 points) Estimate the linear regression line (Round to three decimal places).
(b) (5 points) With the fitted linear regression line in part (a), estimate the mean weight when the height is 200, i.e., x = 200 (Round to three decimal places).
(c) (5 points) Given SST = 3200.93 and SSE = 379.02, determine the proportion of variability explained by the fitted model, i.e., compute the coefficient of determination R².
(d) (20 points) With the fitted linear regression line, the SSE is 379.02 and Sxx = 1299.73. Use t-statistic to test the hypothesis that H0 : ?1 = 3.0 against H1 : ?1 < 3.0. Use a 0.05 level of significance.

Problem 3. (40 points) A random sample of 15 NBA players' heights and weights are being analyzed. The data are recorded as follows:

Player Height, x Weight, y x² xy
1 198 100 39204 19800
2 216 118 46656 25488
3 206 95 42436 19570
4 203 101 41209 20503
5 206 109 42436 22454
6 201 98 40401 19698
7 198 86 39204 17028
8 213 113 45369 24069
9 193 86 37249 16598
10 182 73 33124 13286
11 213 122 45369 25986
12 196 88 38416 17248
13 191 80 36481 15280
14 211 120 44521 25320
15 211 107 44521 22577
Column Sum 3038 1496 616596 304905
Column Average 202.53 99.73

Table 1: NBA height and weight analysis

(a) (10 points) Estimate the linear regression line (Round to three decimal places).
(b) (5 points) With the fitted linear regression line in part (a), estimate the mean weight when the height is 200, i.e., x = 200 (Round to three decimal places).
(c) (5 points) Given SST = 3200.93 and SSE = 379.02, determine the proportion of variability explained by the fitted model, i.e., compute the coefficient of determination R².
(d) (20 points) With the fitted linear regression line, the SSE is 379.02 and Sxx = 1299.73. Use t-statistic to test the hypothesis that H0 : ?1 = 3.0 against H1 : ?1 < 3.0. Use a 0.05 level of significance.

Added by Jimmy A.

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